A New Family of q-Supercongruences Modulo the Fourth Power of a Cyclotomic Polynomial
We establish a new family of q -supercongruences modulo the fourth power of a cyclotomic polynomial, and give several related results. Our main ingredients are q -microscoping and the Chinese remainder theorem for polynomials.
Uložené v:
| Vydané v: | Resultate der Mathematik Ročník 75; číslo 4; s. 155 |
|---|---|
| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Cham
Springer International Publishing
01.12.2020
|
| Predmet: | |
| ISSN: | 1422-6383, 1420-9012, 1420-9012 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | We establish a new family of
q
-supercongruences modulo the fourth power of a cyclotomic polynomial, and give several related results. Our main ingredients are
q
-microscoping and the Chinese remainder theorem for polynomials. |
|---|---|
| AbstractList | We establish a new family of q-supercongruences modulo the fourth power of a cyclotomic polynomial, and give several related results. Our main ingredients are q-microscoping and the Chinese remainder theorem for polynomials.We establish a new family of q-supercongruences modulo the fourth power of a cyclotomic polynomial, and give several related results. Our main ingredients are q-microscoping and the Chinese remainder theorem for polynomials. We establish a new family of q -supercongruences modulo the fourth power of a cyclotomic polynomial, and give several related results. Our main ingredients are q -microscoping and the Chinese remainder theorem for polynomials. We establish a new family of q-supercongruences modulo the fourth power of a cyclotomic polynomial, and give several related results. Our main ingredients are q-microscoping and the Chinese remainder theorem for polynomials. We establish a new family of -supercongruences modulo the fourth power of a cyclotomic polynomial, and give several related results. Our main ingredients are -microscoping and the Chinese remainder theorem for polynomials. |
| ArticleNumber | 155 |
| Author | Guo, Victor J. W. Schlosser, Michael J. |
| Author_xml | – sequence: 1 givenname: Victor J. W. surname: Guo fullname: Guo, Victor J. W. organization: School of Mathematics and Statistics, Huaiyin Normal University – sequence: 2 givenname: Michael J. orcidid: 0000-0002-2612-2431 surname: Schlosser fullname: Schlosser, Michael J. email: michael.schlosser@univie.ac.at organization: Fakultät für Mathematik, Universität Wien |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/33269012$$D View this record in MEDLINE/PubMed |
| BookMark | eNp9kctuFDEQRS0URB7wAyxQL9k0lB-x2xukaJQBpPCQIGvL466eceS2J3Y30fw9nkyCgEVWrrLPvWXVPSVHMUUk5DWFdxRAvS8AwM5bYNACZYq16hk5oaK2uvZH9zVrJe_4MTkt5QbgnDHKXpBjzpncMyfk-qL5infN0o4-7Jo0NLftj3mL2aW4zjNGh6X5kvo5pGbaYLNMc542zfd0h3lP22axcyFNafSu3oZdrJUNL8nzwYaCrx7OM3K9vPy5-NReffv4eXFx1Toh5NQ62_OB95TzAbXoXFd_xzVXVArBhk4A7SWClqAspb1FzVe6Fx2C0L2FleVn5MPBdzuvRuwdxinbYLbZjzbvTLLe_PsS_cas0y-jZNeB1tXg7YNBTrczlsmMvjgMwUZMczFMSKmU5IpV9M3fs_4MedxlBboD4HIqJeNgnJ_s5NN-tA-GgtnHZg6xmRqbuY_NqCpl_0kf3Z8U8YOoVDiuMZubmk6s-35K9RtcsqnW |
| CitedBy_id | crossref_primary_10_1007_s00025_021_01563_7 crossref_primary_10_1007_s13398_021_01171_8 crossref_primary_10_1007_s13398_021_01172_7 crossref_primary_10_1007_s40840_025_01877_7 crossref_primary_10_1007_s00025_025_02369_7 crossref_primary_10_1007_s11139_021_00452_5 crossref_primary_10_1007_s11139_020_00369_5 crossref_primary_10_1007_s11139_022_00597_x crossref_primary_10_1007_s13398_025_01721_4 crossref_primary_10_1515_forum_2023_0409 crossref_primary_10_1007_s13398_022_01364_9 crossref_primary_10_1007_s13398_021_01092_6 crossref_primary_10_1007_s13398_022_01338_x crossref_primary_10_1007_s00025_021_01423_4 crossref_primary_10_1007_s13398_021_01070_y crossref_primary_10_1142_S1793042125500873 crossref_primary_10_1007_s10998_021_00432_8 crossref_primary_10_1007_s10998_021_00437_3 crossref_primary_10_1007_s00009_025_02889_0 crossref_primary_10_1007_s00025_023_01913_7 crossref_primary_10_1080_10236198_2025_2559028 crossref_primary_10_1007_s10998_022_00452_y crossref_primary_10_1007_s40840_025_01912_7 crossref_primary_10_1515_ms_2024_0048 crossref_primary_10_1007_s00025_022_01801_6 crossref_primary_10_1007_s10801_021_01096_w crossref_primary_10_1007_s13226_025_00795_5 crossref_primary_10_1007_s00025_023_01885_8 crossref_primary_10_1007_s00025_021_01350_4 crossref_primary_10_1007_s00025_022_01753_x crossref_primary_10_1216_rmj_2025_55_147 crossref_primary_10_1007_s11139_021_00478_9 |
| Cites_doi | 10.1080/10236198.2019.1622690 10.1090/proc/14301 10.1142/S1793042119501069 10.1007/978-1-4612-0879-2 10.1007/s13398-020-00854-y 10.1016/j.aam.2020.102003 10.1016/j.aam.2020.102078 10.1016/j.jmaa.2019.07.062 10.1142/S1793042120500694 10.2140/pjm.2011.249.405 10.1016/j.jmaa.2020.124022 10.1007/s00025-020-01195-3 10.1017/prm.2018.96 10.1007/s00025-019-1126-4 10.1007/s11425-011-4302-x 10.4064/cm133-1-9 10.1016/j.jnt.2009.01.013 10.1007/s00026-019-00461-8 10.1007/s00025-020-1168-7 10.1016/j.aim.2019.02.008 10.5802/crmath.35 |
| ContentType | Journal Article |
| Copyright | The Author(s) 2020 The Author(s) 2020. |
| Copyright_xml | – notice: The Author(s) 2020 – notice: The Author(s) 2020. |
| DBID | C6C AAYXX CITATION NPM 7X8 5PM |
| DOI | 10.1007/s00025-020-01272-7 |
| DatabaseName | Springer Nature OA Free Journals CrossRef PubMed MEDLINE - Academic PubMed Central (Full Participant titles) |
| DatabaseTitle | CrossRef PubMed MEDLINE - Academic |
| DatabaseTitleList | MEDLINE - Academic PubMed CrossRef |
| Database_xml | – sequence: 1 dbid: NPM name: PubMed url: http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed sourceTypes: Index Database – sequence: 2 dbid: 7X8 name: MEDLINE - Academic url: https://search.proquest.com/medline sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1420-9012 |
| ExternalDocumentID | PMC7688099 33269012 10_1007_s00025_020_01272_7 |
| Genre | Journal Article |
| GrantInformation_xml | – fundername: National Natural Science Foundation of China grantid: 11771175 funderid: http://dx.doi.org/10.13039/501100001809 – fundername: Austrian Science Fund grantid: P32305 funderid: http://dx.doi.org/10.13039/501100002428 – fundername: ; grantid: P32305 – fundername: ; grantid: 11771175 |
| GroupedDBID | -52 -5D -5G -BR -EM -Y2 -~C .86 .VR 06D 0R~ 0VY 123 1N0 203 29P 2J2 2JN 2JY 2KG 2KM 2LR 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5VS 67Z 6NX 78A 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAEWM AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACZOJ ADHHG ADHIR ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFGCZ AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BAPOH BDATZ BGNMA BSONS C6C CAG COF CS3 CSCUP DDRTE DNIVK DPUIP DU5 EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS H13 HF~ HG5 HG6 HLICF HMJXF HQYDN HRMNR HVGLF HZ~ IJ- IKXTQ IWAJR IXC IXD IXE IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV LLZTM M4Y MA- N2Q NB0 NPVJJ NQJWS NU0 O9- O93 O9J OAM P2P P9R PF0 PT4 QOS R89 R9I RHV RIG ROL RPX RSV S16 S1Z S27 S3B SAP SCLPG SDD SDH SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 TSG TSK TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR YNT Z45 ZMTXR ZWQNP ~A9 AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG AEZWR AFDZB AFFHD AFHIU AFKRA AFOHR AGQPQ AHPBZ AHWEU AIXLP ARAPS ATHPR AYFIA AZQEC BENPR BGLVJ CCPQU CITATION DWQXO GNUQQ HCIFZ K7- M2P PHGZM PHGZT PQGLB NPM 7X8 5PM |
| ID | FETCH-LOGICAL-c446t-cad3f3d133fe948c8212393716442f8401d6e09607a11dae93b9d48e049da0ba3 |
| IEDL.DBID | RSV |
| ISICitedReferencesCount | 51 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000573795900001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1422-6383 1420-9012 |
| IngestDate | Tue Nov 04 01:56:29 EST 2025 Thu Sep 04 17:04:03 EDT 2025 Mon Jul 21 06:05:27 EDT 2025 Tue Nov 18 21:08:10 EST 2025 Sat Nov 29 03:47:24 EST 2025 Fri Feb 21 02:37:27 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 4 |
| Keywords | Primary 33D15 supercongruences cyclotomic polynomial 11B65 Basic hypergeometric series congruences Secondary 11A07 microscoping Chinese remainder theorem for polynomials q-congruences q-microscoping |
| Language | English |
| License | The Author(s) 2020. Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c446t-cad3f3d133fe948c8212393716442f8401d6e09607a11dae93b9d48e049da0ba3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| ORCID | 0000-0002-2612-2431 |
| OpenAccessLink | https://link.springer.com/10.1007/s00025-020-01272-7 |
| PMID | 33269012 |
| PQID | 2466776372 |
| PQPubID | 23479 |
| ParticipantIDs | pubmedcentral_primary_oai_pubmedcentral_nih_gov_7688099 proquest_miscellaneous_2466776372 pubmed_primary_33269012 crossref_citationtrail_10_1007_s00025_020_01272_7 crossref_primary_10_1007_s00025_020_01272_7 springer_journals_10_1007_s00025_020_01272_7 |
| PublicationCentury | 2000 |
| PublicationDate | 20201200 |
| PublicationDateYYYYMMDD | 2020-12-01 |
| PublicationDate_xml | – month: 12 year: 2020 text: 20201200 |
| PublicationDecade | 2020 |
| PublicationPlace | Cham |
| PublicationPlace_xml | – name: Cham – name: Switzerland |
| PublicationSubtitle | Resultate der Mathematik |
| PublicationTitle | Resultate der Mathematik |
| PublicationTitleAbbrev | Results Math |
| PublicationTitleAlternate | Results Math |
| PublicationYear | 2020 |
| Publisher | Springer International Publishing |
| Publisher_xml | – name: Springer International Publishing |
| References | GorodetskyOq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-Congruences, with applications to supercongruences and the cyclic sieving phenomenonInt. J. Number Theory20191519191968401552010.1142/S1793042119501069 LongLHypergeometric evaluation identities and supercongruencesPac. J. Math.2011249405418278267710.2140/pjm.2011.249.405 Guo, V.J.W., Schlosser, M.J.: A family of q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial. Israel J. Math. (to appear) RamanujanSModular equations and approximations to π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi $$\end{document}Quart. J. Math. Oxford Ser. (2)19144535037245.1249.01 WangXYueMA q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-analogue of the (A.2) supercongruence of Van Hamme for any prime p≡3(mod4)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p\equiv 3~(\text{ mod } ~ 4)$$\end{document}Int. J. Number Theory20201613251335412047910.1142/S1793042120500694 ZudilinWCongruences for q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-binomial coefficientsAnn. Combin.20192311231135403957910.1007/s00026-019-00461-8 GuoVJWq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-Supercongruences modulo the fourth power of a cyclotomic polynomial via creative microscopingAdv. Appl. Math.2020120102078412195110.1016/j.aam.2020.102078 Van Hamme, L.: Some conjectures concerning partial sums of generalized hypergeometric series. In: p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document}-Adic Functional Analysis (Nijmegen, 1996). Lecture Notes in Pure and Applied Mathematics, vol. 192, pp. 223–236. Dekker, New York (1997) GuoVJWSchlosserMJSome new q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-congruences for truncated basic hypergeometric series: even powersResults Math.2020751404063210.1007/s00025-019-1126-4 GuoVJWSchlosserMJProof of a basic hypergeometric supercongruence modulo the fifth power of a cyclotomic polynomialJ. Differ. Equ. Appl.201925921929399695810.1080/10236198.2019.1622690 LiuJ-COn a congruence involving q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-Catalan numbersC. R. Math. Acad. Sci. Paris2020358211215411817707226778 SunZ-WSuper congruences and Euler numbersSci. China Math.20115425092535286128910.1007/s11425-011-4302-x GuoVJWq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-Analogues of Dwork-type supercongruencesJ. Math. Anal. Appl.2020487124022407853710.1016/j.jmaa.2020.124022 WangXYueMSome q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-supercongruences from Watson’s 8ϕ7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_8\phi _7$$\end{document} transformation formulaResults Math.2020757110.1007/s00025-020-01195-3 NiH-XPanHSome symmetric q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-congruences modulo the square of a cyclotomic polynomialJ. Math. Anal. Appl.2020481123372400719610.1016/j.jmaa.2019.07.062 GuoVJWZudilinWA q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-microscope for supercongruencesAdv. Math.2019346329358391079810.1016/j.aim.2019.02.008 ZudilinWRamanujan-type supercongruencesJ. Number Theory200912918481857252270810.1016/j.jnt.2009.01.013 TaurasoRSome q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-analogs of congruences for central binomial sumsColloq. Math.2013133133143313942010.4064/cm133-1-9 GuoVJWA q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-analogue of the (A.2) supercongruence of Van Hamme for primes p≡1(mod4)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p\equiv 1~(\text{mod}~ 4)$$\end{document}Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat.202011412310.1007/s13398-020-00854-y Guo, V.J.W.: A further q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-analogue of Van Hamme’s (H.2) supercongruence for primes p≡3(mod4)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p\equiv 3~(\text{ mod }~ 4)$$\end{document}. Int. J. Number Theory (to appear) GuoVJWWangS-DSome congruences involving fourth powers of central q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-binomial coefficientsProc. R. Soc. Edinb. Sect. A202015011271138409105510.1017/prm.2018.96 LiuJ-CPetrovFCongruences on sums of q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-binomial coefficientsAdv. Appl. Math.2020116102003405611410.1016/j.aam.2020.102003 GasperGRahmanMEncyclopedia of Mathematics and Its Applications20042CambridgeCambridge University Press BerndtBCRamanujan’s Notebooks, Part IV1994New YorkSpringer10.1007/978-1-4612-0879-2 StraubASupercongruences for polynomial analogs of the Apéry numbersProc. Am. Math. Soc.20191471023103610.1090/proc/14301 Guo, V.J.W., Schlosser, M.J.: Some q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-supercongruences from transformation formulas for basic hypergeometric series. Constr. Approx. (to appear) GuoVJWZudilinWA common q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-analogue of two supercongruencesResults Math.20207546407530010.1007/s00025-020-1168-7 BC Berndt (1272_CR1) 1994 VJW Guo (1272_CR5) 2020; 487 1272_CR11 1272_CR10 VJW Guo (1272_CR8) 2019; 25 X Wang (1272_CR25) 2020; 75 O Gorodetsky (1272_CR3) 2019; 15 VJW Guo (1272_CR4) 2020; 114 H-X Ni (1272_CR18) 2020; 481 Z-W Sun (1272_CR20) 2011; 54 L Long (1272_CR17) 2011; 249 VJW Guo (1272_CR6) 2020; 120 W Zudilin (1272_CR27) 2019; 23 VJW Guo (1272_CR12) 2020; 150 J-C Liu (1272_CR15) 2020; 358 1272_CR23 R Tauraso (1272_CR22) 2013; 133 G Gasper (1272_CR2) 2004 W Zudilin (1272_CR26) 2009; 129 VJW Guo (1272_CR14) 2020; 75 X Wang (1272_CR24) 2020; 16 VJW Guo (1272_CR9) 2020; 75 A Straub (1272_CR21) 2019; 147 1272_CR7 J-C Liu (1272_CR16) 2020; 116 S Ramanujan (1272_CR19) 1914; 45 VJW Guo (1272_CR13) 2019; 346 |
| References_xml | – reference: GasperGRahmanMEncyclopedia of Mathematics and Its Applications20042CambridgeCambridge University Press – reference: RamanujanSModular equations and approximations to π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi $$\end{document}Quart. J. Math. Oxford Ser. (2)19144535037245.1249.01 – reference: GuoVJWSchlosserMJSome new q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-congruences for truncated basic hypergeometric series: even powersResults Math.2020751404063210.1007/s00025-019-1126-4 – reference: GorodetskyOq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-Congruences, with applications to supercongruences and the cyclic sieving phenomenonInt. J. Number Theory20191519191968401552010.1142/S1793042119501069 – reference: TaurasoRSome q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-analogs of congruences for central binomial sumsColloq. Math.2013133133143313942010.4064/cm133-1-9 – reference: BerndtBCRamanujan’s Notebooks, Part IV1994New YorkSpringer10.1007/978-1-4612-0879-2 – reference: Guo, V.J.W.: A further q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-analogue of Van Hamme’s (H.2) supercongruence for primes p≡3(mod4)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p\equiv 3~(\text{ mod }~ 4)$$\end{document}. Int. J. Number Theory (to appear) – reference: Guo, V.J.W., Schlosser, M.J.: A family of q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial. Israel J. Math. (to appear) – reference: LongLHypergeometric evaluation identities and supercongruencesPac. J. Math.2011249405418278267710.2140/pjm.2011.249.405 – reference: GuoVJWWangS-DSome congruences involving fourth powers of central q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-binomial coefficientsProc. R. Soc. Edinb. Sect. A202015011271138409105510.1017/prm.2018.96 – reference: GuoVJWZudilinWA common q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-analogue of two supercongruencesResults Math.20207546407530010.1007/s00025-020-1168-7 – reference: GuoVJWq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-Supercongruences modulo the fourth power of a cyclotomic polynomial via creative microscopingAdv. Appl. Math.2020120102078412195110.1016/j.aam.2020.102078 – reference: GuoVJWq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-Analogues of Dwork-type supercongruencesJ. Math. Anal. Appl.2020487124022407853710.1016/j.jmaa.2020.124022 – reference: NiH-XPanHSome symmetric q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-congruences modulo the square of a cyclotomic polynomialJ. Math. Anal. Appl.2020481123372400719610.1016/j.jmaa.2019.07.062 – reference: SunZ-WSuper congruences and Euler numbersSci. China Math.20115425092535286128910.1007/s11425-011-4302-x – reference: StraubASupercongruences for polynomial analogs of the Apéry numbersProc. Am. Math. Soc.20191471023103610.1090/proc/14301 – reference: WangXYueMA q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-analogue of the (A.2) supercongruence of Van Hamme for any prime p≡3(mod4)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p\equiv 3~(\text{ mod } ~ 4)$$\end{document}Int. J. Number Theory20201613251335412047910.1142/S1793042120500694 – reference: ZudilinWRamanujan-type supercongruencesJ. Number Theory200912918481857252270810.1016/j.jnt.2009.01.013 – reference: Van Hamme, L.: Some conjectures concerning partial sums of generalized hypergeometric series. In: p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document}-Adic Functional Analysis (Nijmegen, 1996). Lecture Notes in Pure and Applied Mathematics, vol. 192, pp. 223–236. Dekker, New York (1997) – reference: LiuJ-COn a congruence involving q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-Catalan numbersC. R. Math. Acad. Sci. Paris2020358211215411817707226778 – reference: GuoVJWA q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-analogue of the (A.2) supercongruence of Van Hamme for primes p≡1(mod4)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p\equiv 1~(\text{mod}~ 4)$$\end{document}Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat.202011412310.1007/s13398-020-00854-y – reference: GuoVJWZudilinWA q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-microscope for supercongruencesAdv. Math.2019346329358391079810.1016/j.aim.2019.02.008 – reference: Guo, V.J.W., Schlosser, M.J.: Some q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-supercongruences from transformation formulas for basic hypergeometric series. Constr. Approx. (to appear) – reference: ZudilinWCongruences for q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-binomial coefficientsAnn. Combin.20192311231135403957910.1007/s00026-019-00461-8 – reference: GuoVJWSchlosserMJProof of a basic hypergeometric supercongruence modulo the fifth power of a cyclotomic polynomialJ. Differ. Equ. Appl.201925921929399695810.1080/10236198.2019.1622690 – reference: LiuJ-CPetrovFCongruences on sums of q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-binomial coefficientsAdv. Appl. Math.2020116102003405611410.1016/j.aam.2020.102003 – reference: WangXYueMSome q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-supercongruences from Watson’s 8ϕ7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_8\phi _7$$\end{document} transformation formulaResults Math.2020757110.1007/s00025-020-01195-3 – volume: 25 start-page: 921 year: 2019 ident: 1272_CR8 publication-title: J. Differ. Equ. Appl. doi: 10.1080/10236198.2019.1622690 – volume: 147 start-page: 1023 year: 2019 ident: 1272_CR21 publication-title: Proc. Am. Math. Soc. doi: 10.1090/proc/14301 – volume: 15 start-page: 1919 year: 2019 ident: 1272_CR3 publication-title: Int. J. Number Theory doi: 10.1142/S1793042119501069 – volume-title: Encyclopedia of Mathematics and Its Applications year: 2004 ident: 1272_CR2 – ident: 1272_CR7 – volume-title: Ramanujan’s Notebooks, Part IV year: 1994 ident: 1272_CR1 doi: 10.1007/978-1-4612-0879-2 – volume: 114 start-page: 123 year: 2020 ident: 1272_CR4 publication-title: Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. doi: 10.1007/s13398-020-00854-y – volume: 116 start-page: 102003 year: 2020 ident: 1272_CR16 publication-title: Adv. Appl. Math. doi: 10.1016/j.aam.2020.102003 – volume: 120 start-page: 102078 year: 2020 ident: 1272_CR6 publication-title: Adv. Appl. Math. doi: 10.1016/j.aam.2020.102078 – ident: 1272_CR11 – volume: 481 start-page: 123372 year: 2020 ident: 1272_CR18 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2019.07.062 – volume: 16 start-page: 1325 year: 2020 ident: 1272_CR24 publication-title: Int. J. Number Theory doi: 10.1142/S1793042120500694 – volume: 249 start-page: 405 year: 2011 ident: 1272_CR17 publication-title: Pac. J. Math. doi: 10.2140/pjm.2011.249.405 – volume: 487 start-page: 124022 year: 2020 ident: 1272_CR5 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2020.124022 – volume: 75 start-page: 71 year: 2020 ident: 1272_CR25 publication-title: Results Math. doi: 10.1007/s00025-020-01195-3 – volume: 150 start-page: 1127 year: 2020 ident: 1272_CR12 publication-title: Proc. R. Soc. Edinb. Sect. A doi: 10.1017/prm.2018.96 – volume: 45 start-page: 350 year: 1914 ident: 1272_CR19 publication-title: Quart. J. Math. Oxford Ser. (2) – ident: 1272_CR23 – volume: 75 start-page: 1 year: 2020 ident: 1272_CR9 publication-title: Results Math. doi: 10.1007/s00025-019-1126-4 – volume: 54 start-page: 2509 year: 2011 ident: 1272_CR20 publication-title: Sci. China Math. doi: 10.1007/s11425-011-4302-x – volume: 133 start-page: 133 year: 2013 ident: 1272_CR22 publication-title: Colloq. Math. doi: 10.4064/cm133-1-9 – volume: 129 start-page: 1848 year: 2009 ident: 1272_CR26 publication-title: J. Number Theory doi: 10.1016/j.jnt.2009.01.013 – volume: 23 start-page: 1123 year: 2019 ident: 1272_CR27 publication-title: Ann. Combin. doi: 10.1007/s00026-019-00461-8 – volume: 75 start-page: 46 year: 2020 ident: 1272_CR14 publication-title: Results Math. doi: 10.1007/s00025-020-1168-7 – ident: 1272_CR10 – volume: 346 start-page: 329 year: 2019 ident: 1272_CR13 publication-title: Adv. Math. doi: 10.1016/j.aim.2019.02.008 – volume: 358 start-page: 211 year: 2020 ident: 1272_CR15 publication-title: C. R. Math. Acad. Sci. Paris doi: 10.5802/crmath.35 |
| SSID | ssj0052212 |
| Score | 2.4360816 |
| Snippet | We establish a new family of
q
-supercongruences modulo the fourth power of a cyclotomic polynomial, and give several related results. Our main ingredients are... We establish a new family of -supercongruences modulo the fourth power of a cyclotomic polynomial, and give several related results. Our main ingredients are... We establish a new family of q-supercongruences modulo the fourth power of a cyclotomic polynomial, and give several related results. Our main ingredients are... |
| SourceID | pubmedcentral proquest pubmed crossref springer |
| SourceType | Open Access Repository Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 155 |
| SubjectTerms | Mathematics Mathematics and Statistics |
| Title | A New Family of q-Supercongruences Modulo the Fourth Power of a Cyclotomic Polynomial |
| URI | https://link.springer.com/article/10.1007/s00025-020-01272-7 https://www.ncbi.nlm.nih.gov/pubmed/33269012 https://www.proquest.com/docview/2466776372 https://pubmed.ncbi.nlm.nih.gov/PMC7688099 |
| Volume | 75 |
| WOSCitedRecordID | wos000573795900001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1420-9012 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0052212 issn: 1422-6383 databaseCode: RSV dateStart: 19970101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1ZS8QwEB68HvTB-1gvIvimhe1BkzyKuPigy-LFvpW0SXShtOu2K-y_d5IesCqCvrZJaCeTme9jMjMA50on0hOCO7wbB45xuY7QSjuiK5NQI4bWtt3byx3t99lwyAd1UljR3HZvQpLWUrfJbl3betXQHRMuRVy4CMvo7pg5jg-PL439RUBRxTgDpFmoXX6dKvPzGvPu6BvG_H5V8ku81Lqh3sb_fmAT1mvYSa4qPdmCBZVtw9p9W7O12IHnK4IWj1SdMEiuybvzOB2rCRLm10l13Zrc53Ka5gRnkR4uWb6RgemyZkYLcj1L0rw0Wc74NJ2ZfGeR7sJz7-bp-tapmy44CTLD0kmE9LUvkbpqxQOWMOPbTNE8BE6eRjroylAZ3kOF60qhuB9zGTCFTEOKbiz8PVjK8kwdANEej11FOYIKnKvcmLsmcZZRzvxQx7IDbiP7KKkrkpvGGGnU1lK2IotQZJEVWUQ7cNHOGVf1OH4dfdZsaYTHxsRCRKbyaRF5QRhStK3U68B-tcXtej5CWoRJ-IbObX47wJTknn-Tjd5saW4kbwwxdwcuGxWIaptQ_PKZh38bfgSrntEie6nmGJZKVIITWEk-ylExOYVFOmSn9kh8AuKWAzc |
| linkProvider | Springer Nature |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1ZS8QwEB50FdQH72M9I_imhe1B2zyKuCjuLuKFbyFtElcorW67wv57J-kBqyLoa5uENpnMfB9zAZxIFQuHc2rRTuRZ2uRaXEll8Y6IfYUYWpl2b0-9YDAIn5_pbZUUltfR7rVL0mjqJtmtY1qvarqj3aWIC2dhzkOLpQP57u6fav2LgKL0cXpIs1C63CpV5uc1ps3RN4z5PVTyi7_UmKHuyv9-YBWWK9hJzks5WYMZma7DUr-p2ZpvwOM5QY1Hyk4YJFPk3bofv8kREuaXURluTfqZGCcZwVmki0sWQ3Kru6zp0ZxcTOIkK3SWMz5NJjrfmSeb8Ni9fLi4sqqmC1aMzLCwYi5c5QqkrkpSL4xDbdt00TwETo5COmgLX2reE3DbFlxSN6LCCyUyDcE7EXe3oJVmqdwBohwa2TKgCCpwrrQjauvE2TCgoeurSLTBrveexVVFct0YI2FNLWWzZQy3jJktY0EbTps5b2U9jl9HH9dHyvDaaF8IT2U2zpnj-X6AujVw2rBdHnGznouQFmESvgmmDr8ZoEtyT79JX4emNDeStxAxdxvOahFglU7If_nM3b8NP4KFq4d-j_WuBzd7sOhoiTIBNvvQKlAgDmA-_ihe89GhuRif9SIFMw |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3da9swED_WbIz2ofvs5nYfGuxtM4k_sK3H0tVsLAmBriVvQraktWDsLHEG-e97J3-wLKMw-mqdZFs66X4_TncH8FGbXPlScpePstAlk-tKo40rRyqPDGJoY8u9XY3j6TSZz_nsjyh-e9u9c0k2MQ2Upamshwtlhn3g28iWYSXqQ65TxIh78DCkokHE1y-uurMYwUXj7wyRcqGmBW3YzL_H2DZNO3hz99rkX75Ta5LSJ_f_madw2MJRdtrozzN4oMvncDDpc7muXsDlKcOTkDUVMlhl2C_3Yr3QS3zJz2VzDZtNKrUuKoa9WIpD1tdsRtXXSFqys01eVDVFP-PTYkNx0LJ4CZfp-Y-zr25bjMHNkTHWbi5VYAKFlNZoHiZ5QjaPkukhoPIN0kRPRZr4UCw9T0nNg4yrMNHIQJQcZTI4gkFZlfo1MOPzzNMxR7CBfbWXcY8CapOYJ0FkMuWA162DyNtM5VQwoxB9jmU7ZQKnTNgpE7EDn_o-iyZPx53SH7rlFbidyEciS12tV8IPoyjGMzf2HXjVLHc_XoBQF-ETtsRbitALUKru7Zby5tqm7EZSlyAWd-Bzpw6iPStWd3zm8f-Jv4fHsy-pGH-bfj-BfZ8Uyt67eQODGvXhLTzKf9c3q-U7u0duAVWtDhc |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+New+Family+of+q-Supercongruences+Modulo+the+Fourth+Power+of+a+Cyclotomic+Polynomial&rft.jtitle=Resultate+der+Mathematik&rft.au=Guo%2C+Victor+J+W&rft.au=Schlosser%2C+Michael+J&rft.date=2020-12-01&rft.issn=1420-9012&rft.eissn=1420-9012&rft.volume=75&rft.issue=4&rft.spage=155&rft_id=info:doi/10.1007%2Fs00025-020-01272-7&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1422-6383&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1422-6383&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1422-6383&client=summon |