Some New q-Congruences for Truncated Basic Hypergeometric Series: Even Powers

We provide several new q -congruences for truncated basic hypergeometric series with the base being an even power of q . Our results mainly concern congruences modulo the square or the cube of a cyclotomic polynomial and complement corresponding ones of an earlier paper containing q -congruences for...

Full description

Saved in:

Bibliographic Details
Published in:	Resultate der Mathematik Vol. 75; no. 1; p. 1
Main Authors:	Guo, Victor J. W., Schlosser, Michael J.
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01.03.2020
Subjects:	Mathematics Mathematics and Statistics Primary 33D15 Andrews’ transformation supercongruences cyclotomic polynomial 11B65 Basic hypergeometric series congruences Secondary 11A07 q-congruences
ISSN:	1422-6383, 1420-9012, 1420-9012
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Abstract	We provide several new q -congruences for truncated basic hypergeometric series with the base being an even power of q . Our results mainly concern congruences modulo the square or the cube of a cyclotomic polynomial and complement corresponding ones of an earlier paper containing q -congruences for truncated basic hypergeometric series with the base being an odd power of q . We also give a number of related conjectures including q -congruences modulo the fifth power of a cyclotomic polynomial and a congruence for a truncated ordinary hypergeometric series modulo the seventh power of a prime greater than 3.
AbstractList	We provide several new q-congruences for truncated basic hypergeometric series with the base being an even power of q. Our results mainly concern congruences modulo the square or the cube of a cyclotomic polynomial and complement corresponding ones of an earlier paper containing q-congruences for truncated basic hypergeometric series with the base being an odd power of q. We also give a number of related conjectures including q-congruences modulo the fifth power of a cyclotomic polynomial and a congruence for a truncated ordinary hypergeometric series modulo the seventh power of a prime greater than 3.We provide several new q-congruences for truncated basic hypergeometric series with the base being an even power of q. Our results mainly concern congruences modulo the square or the cube of a cyclotomic polynomial and complement corresponding ones of an earlier paper containing q-congruences for truncated basic hypergeometric series with the base being an odd power of q. We also give a number of related conjectures including q-congruences modulo the fifth power of a cyclotomic polynomial and a congruence for a truncated ordinary hypergeometric series modulo the seventh power of a prime greater than 3. We provide several new q -congruences for truncated basic hypergeometric series with the base being an even power of q . Our results mainly concern congruences modulo the square or the cube of a cyclotomic polynomial and complement corresponding ones of an earlier paper containing q -congruences for truncated basic hypergeometric series with the base being an odd power of q . We also give a number of related conjectures including q -congruences modulo the fifth power of a cyclotomic polynomial and a congruence for a truncated ordinary hypergeometric series modulo the seventh power of a prime greater than 3. We provide several new q-congruences for truncated basic hypergeometric series with the base being an even power of q. Our results mainly concern congruences modulo the square or the cube of a cyclotomic polynomial and complement corresponding ones of an earlier paper containing q-congruences for truncated basic hypergeometric series with the base being an odd power of q. We also give a number of related conjectures including q-congruences modulo the fifth power of a cyclotomic polynomial and a congruence for a truncated ordinary hypergeometric series modulo the seventh power of a prime greater than 3. We provide several new -congruences for truncated basic hypergeometric series with the base being an even power of . Our results mainly concern congruences modulo the square or the cube of a cyclotomic polynomial and complement corresponding ones of an earlier paper containing -congruences for truncated basic hypergeometric series with the base being an odd power of . We also give a number of related conjectures including -congruences modulo the fifth power of a cyclotomic polynomial and a congruence for a truncated ordinary hypergeometric series modulo the seventh power of a prime greater than 3.
ArticleNumber	1
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/32214886$$D View this record in MEDLINE/PubMed
BookMark	eNp9kUtP3DAUhS1EVR7tD2BTZdmNwdeJ44QFUjviUYmXBF1bjnM9NcrYg52A-Pf1MFAVFqyurXu-c6R7dsimDx4J2QO2D4zJg8QY44IyaCkAr2m1Qbah4oy2DPjm85vTumzKLbKT0h1jgnPgn8lWmWfVNPU2ubgJCywu8bG4p7Pg53FCbzAVNsTiNk7e6BH74qdOzhRnT0uMc8zAGPP3BqPDdFgcP6AvrsMjxvSFfLJ6SPj1Ze6S3yfHt7Mzen51-mv245yaquIjxYaVohdNK6QGYEbUkltb9Z2wvRS10W3Xyx4s6Ka12JWoeScRoJec1WhtuUuO1r7LqVtgb9CPUQ9qGd1CxycVtFNvN979UfPwoCTLURKywfcXgxjuJ0yjWrhkcBi0xzAlxcsm37EWz9Jv_2f9C3m9YRbItcDEkFJEq4wb9ejCKtoNCphataXWbancllq1papMwjvy1fwjhq-ZlLV-jlHdhSn6fO0PoL-yFqdt
CitedBy_id	crossref_primary_10_1007_s00025_021_01563_7 crossref_primary_10_1016_j_jmaa_2022_126062 crossref_primary_10_1007_s13398_020_00935_y crossref_primary_10_1007_s10998_020_00377_4 crossref_primary_10_1016_j_jmaa_2020_124062 crossref_primary_10_1007_s00025_020_1168_7 crossref_primary_10_1007_s11139_022_00597_x crossref_primary_10_1007_s13398_025_01721_4 crossref_primary_10_1016_j_jmaa_2020_124022 crossref_primary_10_1016_j_jmaa_2020_124068 crossref_primary_10_1007_s00025_021_01469_4 crossref_primary_10_1007_s13398_021_01070_y crossref_primary_10_1007_s11856_020_2081_1 crossref_primary_10_1007_s00025_020_01195_3 crossref_primary_10_1007_s10998_021_00432_8 crossref_primary_10_1016_j_aam_2020_102003 crossref_primary_10_1007_s00025_020_01272_7 crossref_primary_10_1007_s10998_020_00341_2 crossref_primary_10_1007_s00365_020_09524_z crossref_primary_10_1007_s40840_025_01912_7 crossref_primary_10_1007_s10231_022_01187_w crossref_primary_10_1016_j_aam_2020_102078 crossref_primary_10_1007_s11139_021_00400_3 crossref_primary_10_1017_S0004972720000118 crossref_primary_10_1007_s00025_021_01402_9 crossref_primary_10_1007_s13226_025_00795_5 crossref_primary_10_1016_j_jmaa_2020_124402 crossref_primary_10_1016_j_aam_2020_102016 crossref_primary_10_1007_s00025_020_01203_6 crossref_primary_10_1007_s12044_020_00591_7 crossref_primary_10_1007_s10114_023_1152_8
Cites_doi	10.4064/aa127-1-2 10.4064/cm7686-11-2018 10.4064/aa-86-1-17-26 10.1016/j.jnt.2016.09.011 10.1090/S0002-9939-08-09389-1 10.1016/j.jnt.2009.01.013 10.1016/j.aim.2019.02.008 10.1016/j.jmaa.2017.09.022 10.1016/j.jnt.2014.07.013 10.1017/CBO9780511526251 10.1007/s00013-008-2828-0 10.1090/hmath/009 10.1186/s40687-015-0037-6 10.4064/cm133-1-9 10.1142/S1793042118501038 10.1080/10236198.2019.1622690 10.4064/aa180624-16-12 10.1080/10236198.2018.1485669 10.1016/B978-0-12-064850-4.50008-2 10.1016/j.jmaa.2015.08.009 10.1142/S1793042119501069 10.2140/pjm.2011.249.405 10.1142/S1793042118501701 10.1080/10236198.2019.1572129 10.3390/sym11020268 10.1090/proc/14301 10.1007/s00025-019-1056-1 10.1090/proc/14664
ContentType	Journal Article
Copyright	The Author(s) 2019 The Author(s) 2019.
Copyright_xml	– notice: The Author(s) 2019 – notice: The Author(s) 2019.
DBID	C6C AAYXX CITATION NPM 7X8 5PM
DOI	10.1007/s00025-019-1126-4
DatabaseName	Springer Nature OA Free Journals CrossRef PubMed MEDLINE - Academic PubMed Central (Full Participant titles)
DatabaseTitle	CrossRef PubMed MEDLINE - Academic
DatabaseTitleList	MEDLINE - Academic CrossRef PubMed
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	PMC7067271 32214886 10_1007_s00025_019_1126_4
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: P 32305 funderid: http://dx.doi.org/10.13039/501100002428 – fundername: ; grantid: P 32305 – 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-c442t-e8035d58957a110c5672ff4db5fd756ca9bd7d1f1a89feb3ea2b7e11d7206eff3
IEDL.DBID	RSV
ISICitedReferencesCount	27
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000499705300001&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 01:58:59 EST 2025 Sun Nov 09 12:51:26 EST 2025 Mon Jul 21 06:07:21 EDT 2025 Tue Nov 18 22:28:48 EST 2025 Sat Nov 29 03:47:23 EST 2025 Fri Feb 21 02:37:27 EST 2025
IsDoiOpenAccess	true
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Issue	1
Keywords	Primary 33D15 Andrews’ transformation supercongruences cyclotomic polynomial 11B65 Basic hypergeometric series congruences Secondary 11A07 q-congruences
Language	English
License	The Author(s) 2019. Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c442t-e8035d58957a110c5672ff4db5fd756ca9bd7d1f1a89feb3ea2b7e11d7206eff3
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/s00025-019-1126-4
PMID	32214886
PQID	2384206571
PQPubID	23479
ParticipantIDs	pubmedcentral_primary_oai_pubmedcentral_nih_gov_7067271 proquest_miscellaneous_2384206571 pubmed_primary_32214886 crossref_citationtrail_10_1007_s00025_019_1126_4 crossref_primary_10_1007_s00025_019_1126_4 springer_journals_10_1007_s00025_019_1126_4
PublicationCentury	2000
PublicationDate	2020-03-01
PublicationDateYYYYMMDD	2020-03-01
PublicationDate_xml	– month: 03 year: 2020 text: 2020-03-01 day: 01
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	Sun (CR28) 2015; 147 Osburn, Zudilin (CR25) 2016; 433 Gasper, Rahman (CR4) 2004 Straub (CR27) 2019; 147 McCarthy, Osburn (CR21) 2008; 91 CR17 Long (CR20) 2011; 249 CR34 Guo (CR11) 2019; 190 CR33 Morita (CR22) 1975; 22 Andrews (CR1) 1975 Swisher (CR30) 2015; 2 Guo, Liu (CR13) 2018; 24 Ni, Pan (CR24) 2018; 14 Sun (CR29) 2019; 158 Van Hamme (CR32) 1997 Calkin (CR3) 1998; 86 Guo (CR9) 2019; 74 Zudilin (CR35) 2009; 129 Guo, Zudilin (CR18) 2019; 346 Guo, Schlosser (CR16) 2019; 25 Tauraso (CR31) 2013; 133 CR5 Hardy (CR19) 1923; 21 Guo, Jouhet, Zeng (CR12) 2007; 127 Guo, Pan, Zhang (CR14) 2017; 174 Guo (CR7) 2018; 458 Guo (CR10) 2019; 25 Gorodetsky (CR6) 2019; 15 Guo (CR8) 2019; 15 Mortenson (CR23) 2008; 136 Ramanujan (CR26) 1914; 2 Berndt, Rankin (CR2) 1995 Guo, Schlosser (CR15) 2019; 11 VJW Guo (1126_CR12) 2007; 127 H-X Ni (1126_CR24) 2018; 14 L Van Hamme (1126_CR32) 1997 VJW Guo (1126_CR10) 2019; 25 VJW Guo (1126_CR14) 2017; 174 W Zudilin (1126_CR35) 2009; 129 G Gasper (1126_CR4) 2004 Y Morita (1126_CR22) 1975; 22 O Gorodetsky (1126_CR6) 2019; 15 VJW Guo (1126_CR18) 2019; 346 D McCarthy (1126_CR21) 2008; 91 George E. Andrews (1126_CR1) 1975 A Straub (1126_CR27) 2019; 147 1126_CR33 1126_CR34 L Long (1126_CR20) 2011; 249 VJW Guo (1126_CR8) 2019; 15 VJW Guo (1126_CR15) 2019; 11 E Mortenson (1126_CR23) 2008; 136 1126_CR5 VJW Guo (1126_CR7) 2018; 458 VJW Guo (1126_CR13) 2018; 24 S Ramanujan (1126_CR26) 1914; 2 VJW Guo (1126_CR16) 2019; 25 GH Hardy (1126_CR19) 1923; 21 Z-W Sun (1126_CR29) 2019; 158 NJ Calkin (1126_CR3) 1998; 86 VJW Guo (1126_CR9) 2019; 74 BC Berndt (1126_CR2) 1995 R Osburn (1126_CR25) 2016; 433 R Tauraso (1126_CR31) 2013; 133 1126_CR17 Z-W Sun (1126_CR28) 2015; 147 VJW Guo (1126_CR11) 2019; 190 H Swisher (1126_CR30) 2015; 2
References_xml	– volume: 2 start-page: 350 issue: 45 year: 1914 end-page: 372 ident: CR26 article-title: Modular equations and approximations to publication-title: Q. J. Math. Oxf. Ser. – start-page: 223 year: 1997 end-page: 236 ident: CR32 article-title: Some conjectures concerning partial sums of generalized hypergeometric series publication-title: -Adic Functional Analysis (Nijmegen 1996), Lecture Notes in Pure and Applied Mathematics – volume: 127 start-page: 17 year: 2007 end-page: 31 ident: CR12 article-title: Factors of alternating sums of products of binomial and -binomial coefficients publication-title: Acta Arith. doi: 10.4064/aa127-1-2 – volume: 158 start-page: 313 year: 2019 end-page: 320 ident: CR29 article-title: Two -analogues of Euler’s formula publication-title: Colloq. Math. doi: 10.4064/cm7686-11-2018 – volume: 86 start-page: 17 year: 1998 end-page: 26 ident: CR3 article-title: Factors of sums of powers of binomial coefficients publication-title: Acta Arith. doi: 10.4064/aa-86-1-17-26 – volume: 174 start-page: 358 year: 2017 end-page: 368 ident: CR14 article-title: The Rodriguez–Villegas type congruences for truncated -hypergeometric functions publication-title: J. Number Theory doi: 10.1016/j.jnt.2016.09.011 – volume: 136 start-page: 4321 issue: 12 year: 2008 end-page: 4328 ident: CR23 article-title: A -adic supercongruence conjecture of van Hamme publication-title: Proc. Am. Math. Soc. doi: 10.1090/S0002-9939-08-09389-1 – volume: 129 start-page: 1848 issue: 8 year: 2009 end-page: 1857 ident: CR35 article-title: Ramanujan-type supercongruences publication-title: J. Number Theory doi: 10.1016/j.jnt.2009.01.013 – volume: 21 start-page: 492 issue: 2 year: 1923 end-page: 503 ident: CR19 article-title: A chapter from Ramanujan’s note-book publication-title: Proc. Camb. Philos. Soc. – volume: 346 start-page: 329 year: 2019 end-page: 358 ident: CR18 article-title: A -microscope for supercongruences publication-title: Adv. Math. doi: 10.1016/j.aim.2019.02.008 – ident: CR33 – volume: 458 start-page: 590 year: 2018 end-page: 600 ident: CR7 article-title: A -analogue of a Ramanujan-type supercongruence involving central binomial coefficients publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2017.09.022 – volume: 147 start-page: 326 year: 2015 end-page: 341 ident: CR28 article-title: Supercongruences motivated by publication-title: J. Number Theory doi: 10.1016/j.jnt.2014.07.013 – year: 2004 ident: CR4 publication-title: Basic Hypergeometric Series doi: 10.1017/CBO9780511526251 – volume: 91 start-page: 492 issue: 6 year: 2008 end-page: 504 ident: CR21 article-title: A -adic analogue of a formula of Ramanujan publication-title: Arch. Math. (Basel) doi: 10.1007/s00013-008-2828-0 – year: 1995 ident: CR2 publication-title: Ramanujan, Letters and Commentary, History of Mathematics doi: 10.1090/hmath/009 – volume: 2 start-page: 18 year: 2015 ident: CR30 article-title: On the supercongruence conjectures of van Hamme publication-title: Res. Math. Sci. doi: 10.1186/s40687-015-0037-6 – volume: 133 start-page: 133 year: 2013 end-page: 143 ident: CR31 article-title: Some -analogs of congruences for central binomial sums publication-title: Colloq. Math. doi: 10.4064/cm133-1-9 – volume: 14 start-page: 1699 year: 2018 end-page: 1707 ident: CR24 article-title: On a conjectured -congruence of Guo and Zeng publication-title: Int. J. Number Theory doi: 10.1142/S1793042118501038 – volume: 25 start-page: 921 year: 2019 end-page: 929 ident: CR16 article-title: Proof of a basic hypergeometric supercongruence modulo the fifth power of a cyclotomic polynomial publication-title: J. Differ. Equ. Appl. doi: 10.1080/10236198.2019.1622690 – volume: 190 start-page: 381 year: 2019 end-page: 393 ident: CR11 article-title: Some -congruences with parameters publication-title: Acta Arith. doi: 10.4064/aa180624-16-12 – volume: 24 start-page: 1368 year: 2018 end-page: 1373 ident: CR13 article-title: -Analogues of two Ramanujan-type formulas for publication-title: J. Differ. Equ. Appl. doi: 10.1080/10236198.2018.1485669 – start-page: 191 year: 1975 end-page: 224 ident: CR1 article-title: Problems and Prospects for Basic Hypergeometric Functions publication-title: Theory and Application of Special Functions doi: 10.1016/B978-0-12-064850-4.50008-2 – ident: CR17 – volume: 433 start-page: 706 year: 2016 end-page: 711 ident: CR25 article-title: On the (K.2) supercongruence of Van Hamme publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2015.08.009 – volume: 15 start-page: 1919 year: 2019 end-page: 1968 ident: CR6 article-title: -Congruences, with applications to supercongruences and the cyclic sieving phenomenon publication-title: Int. J. Number Theory doi: 10.1142/S1793042119501069 – ident: CR34 – volume: 249 start-page: 405 issue: 2 year: 2011 end-page: 418 ident: CR20 article-title: Hypergeometric evaluation identities and supercongruences publication-title: Pac. J. Math. doi: 10.2140/pjm.2011.249.405 – ident: CR5 – volume: 15 start-page: 29 year: 2019 end-page: 36 ident: CR8 article-title: A -analogue of the (I.2) supercongruence of Van Hamme publication-title: Int. J. Number Theory doi: 10.1142/S1793042118501701 – volume: 25 start-page: 342 year: 2019 end-page: 350 ident: CR10 article-title: A -analogue of a curious supercongruence of Guillera and Zudilin publication-title: J. Differ. Equ. Appl. doi: 10.1080/10236198.2019.1572129 – volume: 11 start-page: 268 issue: 2 year: 2019 ident: CR15 article-title: Some new -congruences for truncated basic hypergeometric series publication-title: Symmetry doi: 10.3390/sym11020268 – volume: 147 start-page: 1023 year: 2019 end-page: 1036 ident: CR27 article-title: Supercongruences for polynomial analogs of the Apéry numbers publication-title: Proc. Am. Math. Soc. doi: 10.1090/proc/14301 – volume: 74 start-page: 131 year: 2019 ident: CR9 article-title: Common -analogues of some different supercongruences publication-title: Results Math. doi: 10.1007/s00025-019-1056-1 – volume: 22 start-page: 255 year: 1975 end-page: 266 ident: CR22 article-title: A -adic supercongruence of the function publication-title: J. Fac. Sci. Univ. Tokyo – start-page: 223 volume-title: $$p$$-Adic Functional Analysis (Nijmegen 1996), Lecture Notes in Pure and Applied Mathematics year: 1997 ident: 1126_CR32 – volume: 346 start-page: 329 year: 2019 ident: 1126_CR18 publication-title: Adv. Math. doi: 10.1016/j.aim.2019.02.008 – volume: 25 start-page: 921 year: 2019 ident: 1126_CR16 publication-title: J. Differ. Equ. Appl. doi: 10.1080/10236198.2019.1622690 – volume: 22 start-page: 255 year: 1975 ident: 1126_CR22 publication-title: J. Fac. Sci. Univ. Tokyo – volume: 458 start-page: 590 year: 2018 ident: 1126_CR7 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2017.09.022 – volume: 190 start-page: 381 year: 2019 ident: 1126_CR11 publication-title: Acta Arith. doi: 10.4064/aa180624-16-12 – volume: 129 start-page: 1848 issue: 8 year: 2009 ident: 1126_CR35 publication-title: J. Number Theory doi: 10.1016/j.jnt.2009.01.013 – start-page: 191 volume-title: Theory and Application of Special Functions year: 1975 ident: 1126_CR1 doi: 10.1016/B978-0-12-064850-4.50008-2 – volume-title: Ramanujan, Letters and Commentary, History of Mathematics year: 1995 ident: 1126_CR2 doi: 10.1090/hmath/009 – volume: 15 start-page: 1919 year: 2019 ident: 1126_CR6 publication-title: Int. J. Number Theory doi: 10.1142/S1793042119501069 – ident: 1126_CR33 – volume: 11 start-page: 268 issue: 2 year: 2019 ident: 1126_CR15 publication-title: Symmetry doi: 10.3390/sym11020268 – volume: 147 start-page: 326 year: 2015 ident: 1126_CR28 publication-title: J. Number Theory doi: 10.1016/j.jnt.2014.07.013 – volume: 74 start-page: 131 year: 2019 ident: 1126_CR9 publication-title: Results Math. doi: 10.1007/s00025-019-1056-1 – ident: 1126_CR5 – volume: 249 start-page: 405 issue: 2 year: 2011 ident: 1126_CR20 publication-title: Pac. J. Math. doi: 10.2140/pjm.2011.249.405 – volume: 91 start-page: 492 issue: 6 year: 2008 ident: 1126_CR21 publication-title: Arch. Math. (Basel) doi: 10.1007/s00013-008-2828-0 – volume: 25 start-page: 342 year: 2019 ident: 1126_CR10 publication-title: J. Differ. Equ. Appl. doi: 10.1080/10236198.2019.1572129 – volume: 86 start-page: 17 year: 1998 ident: 1126_CR3 publication-title: Acta Arith. doi: 10.4064/aa-86-1-17-26 – volume: 127 start-page: 17 year: 2007 ident: 1126_CR12 publication-title: Acta Arith. doi: 10.4064/aa127-1-2 – volume: 158 start-page: 313 year: 2019 ident: 1126_CR29 publication-title: Colloq. Math. doi: 10.4064/cm7686-11-2018 – volume: 2 start-page: 350 issue: 45 year: 1914 ident: 1126_CR26 publication-title: Q. J. Math. Oxf. Ser. – volume-title: Basic Hypergeometric Series year: 2004 ident: 1126_CR4 doi: 10.1017/CBO9780511526251 – ident: 1126_CR34 doi: 10.1090/proc/14664 – volume: 133 start-page: 133 year: 2013 ident: 1126_CR31 publication-title: Colloq. Math. doi: 10.4064/cm133-1-9 – volume: 2 start-page: 18 year: 2015 ident: 1126_CR30 publication-title: Res. Math. Sci. doi: 10.1186/s40687-015-0037-6 – volume: 147 start-page: 1023 year: 2019 ident: 1126_CR27 publication-title: Proc. Am. Math. Soc. doi: 10.1090/proc/14301 – volume: 14 start-page: 1699 year: 2018 ident: 1126_CR24 publication-title: Int. J. Number Theory doi: 10.1142/S1793042118501038 – volume: 21 start-page: 492 issue: 2 year: 1923 ident: 1126_CR19 publication-title: Proc. Camb. Philos. Soc. – ident: 1126_CR17 – volume: 15 start-page: 29 year: 2019 ident: 1126_CR8 publication-title: Int. J. Number Theory doi: 10.1142/S1793042118501701 – volume: 433 start-page: 706 year: 2016 ident: 1126_CR25 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2015.08.009 – volume: 24 start-page: 1368 year: 2018 ident: 1126_CR13 publication-title: J. Differ. Equ. Appl. doi: 10.1080/10236198.2018.1485669 – volume: 174 start-page: 358 year: 2017 ident: 1126_CR14 publication-title: J. Number Theory doi: 10.1016/j.jnt.2016.09.011 – volume: 136 start-page: 4321 issue: 12 year: 2008 ident: 1126_CR23 publication-title: Proc. Am. Math. Soc. doi: 10.1090/S0002-9939-08-09389-1
SSID	ssj0052212
Score	2.3910427
Snippet	We provide several new q -congruences for truncated basic hypergeometric series with the base being an even power of q . Our results mainly concern congruences... We provide several new -congruences for truncated basic hypergeometric series with the base being an even power of . Our results mainly concern congruences... We provide several new q-congruences for truncated basic hypergeometric series with the base being an even power of q. Our results mainly concern congruences...
SourceID	pubmedcentral proquest pubmed crossref springer
SourceType	Open Access Repository Aggregation Database Index Database Enrichment Source Publisher
StartPage	1
SubjectTerms	Mathematics Mathematics and Statistics
Title	Some New q-Congruences for Truncated Basic Hypergeometric Series: Even Powers
URI	https://link.springer.com/article/10.1007/s00025-019-1126-4 https://www.ncbi.nlm.nih.gov/pubmed/32214886 https://www.proquest.com/docview/2384206571 https://pubmed.ncbi.nlm.nih.gov/PMC7067271
Volume	75
WOSCitedRecordID	wos000499705300001&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 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/eLvHCXMwnV3JTsMwEB2xHeDAvpRNRuIEspSkTuxwg6qICwjRgnqLEi-ABCk0he9n7CxS2SQ4x7asGXvmTWb8BuBQeqEXKRlQ9L0YoARGU4FegEYsllogRtWybDbBr67EYBBfV--4i7ravU5JOkvdPHbzXOtVhCTUPnuhbBpm0dsJextvene1-UU8UaY4GUZZeLjadSrzuyUmndEXhPm1UPJTttQ5ofOlf21_GRYrzElOy0OyAlM6X4WFy4awtViDy97wWRO0eOSVdob5_aisryYIaUl_9GaZY7UiZynqlFxg6Dq61zjBsvsT-39NFyeki2aTXLuma-twe97tdy5o1WmBSsaCMdXCa4cqFHHIU8QDMox4YAxTWWgUDyOZxpniyjd-KmKD4bdOg4xr31c8QG0a096AmXyY6y0gPBBKusa6vkQwaLIUMRWXmZdmgknNWuDVIk9kRUNuu2E8JQ2BspNUgpJKrKQSnHLUTHkpOTh-G3xQ6zHBm2LTH2muh29FguCE4XZD7rdgs9RrsxyaNYwLRdQCPqHxZoBl4Z78kj8-ODZu7pLZuOZxrfekMgPFz7vc_tPoHZgPbJjvSt92YWaMh2AP5uT7-LEY7cM0H4h9dwk-AIDC_3w
linkProvider	Springer Nature
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LT9wwEB61FKn0QHl3aQEjcSqylGSd2OEGCLQIdoVgQdysxA9AgizdLP39jJ2HtIVWKufYljVjz3yTGX8DsKOCOEi0iij6XgxQImuoQC9AE5YqIxCjGlU1m-CDgbi5Sc_rd9xlU-3epCS9pW4fuwW-9SpCEuqevVD2ET4xdFiuju_i8roxv4gnqhQnwygLD1e3SWW-tcS0M3qFMF8XSv6RLfVO6Pjru7a_APM15iT71SFZhA-mWIIv_ZawtVyG_uXo0RC0eOQXPRwVt-OqvpogpCXD8bNjjjWaHGSoU9LD0HV8a3CCY_cn7v-aKffIEZpNcu6brq3A1fHR8LBH604LVDEWTagRQTfWsUhjniEeUHHCI2uZzmOreZyoLM0116ENM5FaDL9NFuXchKHmEWrT2u4qzBSjwnwDwiOhlW-sGyoEgzbPEFNxlQdZLpgyrANBI3Kpahpy1w3jQbYEyl5SEiUlnaQkTvnZTnmqODj-NXi70aPEm-LSH1lhRs-lRHDCcLsxDzuwVum1XQ7NGsaFIukAn9J4O8CxcE9_Ke7vPBs398lsXHO30buszUD5912u_9foLfjcG_bP5NnJ4PQ7zEUu5PdlcD9gZoIHYgNm1e_JfTne9FfhBX2aAYc
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3db9MwED-NDSH2wMbnCmMzEk8gq0nqxA5v0K3qtLWq1IH6ZiX-KJMgHU23v39n50MqHUiI59iWc3c-_85n_w7gvQriINEqorj3YoASWUMF7gI0YakyAjGqUVWxCT4ei9ksndR1TsvmtnuTkqzeNDiWpmLVvda22z58C3wZVoQn1D2BoewB7DBXM8iF69NvjStGbFGlOxlGXGhovSated8Q6xvTBtrcvDT5W-bUb0iDvf_-lX14UmNR8rkynqewZYpnsDtqiVzL5zCaLn4agp6Q_KL9RTFfVveuCUJdcrm8cYyyRpMvGeqaDDGkXc4NdnCs_8Sdu5nyEzlFd0omvhjbC_g6OL3sD2ldgYEqxqIVNSLoxToWacwzxAkqTnhkLdN5bDWPE5WlueY6tGEmUothucminJsw1DxCLVvbewnbxaIwB0B4JLTyBXdDhSDR5hliLa7yIMsFU4Z1IGjEL1VNT-6qZPyQLbGyl5RESUknKYldPrRdritujr81ftfoVOIKcmmRrDCLm1IiaGE43ZiHHXhV6bgdDt0dxosi6QBf037bwLFzr38prr57lm7uk9w45sfGBmTtHso_z_L1P7U-hkeTk4G8OBufv4HHkTsJ8LfjDmF7hfbwFh6q29VVuTzyq-IOPIoKaw
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=Some+New+q-Congruences+for+Truncated+Basic+Hypergeometric+Series%3A+Even+Powers&rft.jtitle=Resultate+der+Mathematik&rft.au=Guo%2C+Victor+J+W&rft.au=Schlosser%2C+Michael+J&rft.date=2020-03-01&rft.issn=1420-9012&rft.eissn=1420-9012&rft.volume=75&rft.issue=1&rft.spage=1&rft_id=info:doi/10.1007%2Fs00025-019-1126-4&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