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.
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| Published in: | Resultate der Mathematik Vol. 75; no. 4; p. 155 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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01.12.2020
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| ISSN: | 1422-6383, 1420-9012, 1420-9012 |
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| 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$$D View this record in MEDLINE/PubMed |
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| Cites_doi | 10.1080/10236198.2019.1622690 10.1090/proc/14301 10.1142/S1793042119501069 10.1007/978-1-4612-0879-2 10.1007/s13398-020-00854-y 10.1016/j.aam.2020.102003 10.1016/j.aam.2020.102078 10.1016/j.jmaa.2019.07.062 10.1142/S1793042120500694 10.2140/pjm.2011.249.405 10.1016/j.jmaa.2020.124022 10.1007/s00025-020-01195-3 10.1017/prm.2018.96 10.1007/s00025-019-1126-4 10.1007/s11425-011-4302-x 10.4064/cm133-1-9 10.1016/j.jnt.2009.01.013 10.1007/s00026-019-00461-8 10.1007/s00025-020-1168-7 10.1016/j.aim.2019.02.008 10.5802/crmath.35 |
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| Keywords | Primary 33D15 supercongruences cyclotomic polynomial 11B65 Basic hypergeometric series congruences Secondary 11A07 microscoping Chinese remainder theorem for polynomials q-congruences q-microscoping |
| Language | English |
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| References | GorodetskyOq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$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. 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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... |
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| Title | A New Family of q-Supercongruences Modulo the Fourth Power of a Cyclotomic Polynomial |
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