Some q-supercongruences modulo the square and cube of a cyclotomic polynomial

被引：6

作者：

Guo, Victor J. W. ^{[1
]}

Schlosser, Michael J. ^{[2
]}

机构：

[1] Huaiyin Normal Univ, Sch Math & Stat, Huaian 223300, Jiangsu, Peoples R China

[2] Univ Wien, Fak Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

来源：

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2021年 / 115卷 / 03期

基金：

奥地利科学基金会; 中国国家自然科学基金;

关键词：

Basic hypergeometric series; Supercongruences; q-congruences; Cyclotomic polynomial; Andrews' transformation; Gasper's summation; CONGRUENCES;

D O I：

10.1007/s13398-021-01070-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Two q-supercongruences of truncated basic hypergeometric series containing two free parameters are established by employing specific identities for basic hypergeometric series. The results partly extend two q-supercongruences that were earlier conjectured by the same authors and involve q-supercongruences modulo the square and the cube of a cyclotomic polynomial. One of the newly proved q-supercongruences is even conjectured to hold modulo the fourth power of a cyclotomic polynomial.

引用

页数：9

共 33 条

[1]

ANDREWS GE, 1975, THEORY APPL SPECIAL, P191

[2]

Borwein JM., 1998, PI AGM CANADIAN MATH

[3]

Gasper G., 1997, SERIES RELATED TOPIC, P55, DOI DOI 10.1090/FIC/014/03

[4]

Gasper G., 2004, Encycl. Math. Appl., Vsecond

[5] q-Congruences, with applications to supercongruences and the cyclic sieving phenomenon [J].

Gorodetsky, Ofir .

INTERNATIONAL JOURNAL OF NUMBER THEORY, 2019, 15 (09) :1919-1968

[6] Proof of a generalization of the (C.2) supercongruence of Van Hamme [J].

Guo, Victor J. W. .

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2021, 115 (02)

[7] Dwork-type supercongruences through a creative q-microscope [J].

Guo, Victor J. W. ;

Zudilin, Wadim .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 2021, 178

[8] Some q-Supercongruences from Transformation Formulas for Basic Hypergeometric Series [J].

Guo, Victor J. W. ;

Schlosser, Michael J. .

CONSTRUCTIVE APPROXIMATION, 2021, 53 (01) :155-200

[9] A family of q-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial [J].

Guo, Victor J. W. ;

Schlosser, Michael J. .

ISRAEL JOURNAL OF MATHEMATICS, 2020, 240 (02) :821-835

[10] Proof of Some q-Supercongruences Modulo the Fourth Power of a Cyclotomic Polynomial [J].

Guo, Victor J. W. .

RESULTS IN MATHEMATICS, 2020, 75 (03)

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