Two q-congruences from Carlitz's formula

被引：9

作者：

Gu, Cheng-Yang ^{[1
]}

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

机构：

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

来源：

PERIODICA MATHEMATICA HUNGARICA | 2021年 / 82卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Congruence; q-congruence; Cyclotomic polynomial; Carlitz's formula;

D O I：

10.1007/s10998-020-00341-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Recently, using a formula of Carlitz, the second author proved a q-congruence conjectured by Tauraso. In this note we utilize Carlitz's formula to prove two more similar q-congruences. We also propose a conjectural q-congruence that refines one of our q-congruences.

引用

页码：82 / 86

页数：5

共 16 条

[1] Carlitz L., 1974, FIBONACCI QUART, V12, P369
[2] Gasper G., 2004, ENCY MATH ITS APPL, P96
[3] q-Congruences, with applications to supercongruences and the cyclic sieving phenomenon
Gorodetsky, Ofir
[J]. INTERNATIONAL JOURNAL OF NUMBER THEORY, 2019, 15 (09) : 1919 - 1968
[4] q-Analogues of Two Supercongruences of Z.-W. Sun
Gu, Cheng-Yang
Guo, Victor J. W.
[J]. CZECHOSLOVAK MATHEMATICAL JOURNAL, 2020, 70 (03) : 757 - 765
[5] A family of q-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial
Guo, Victor J. W.
Schlosser, Michael J.
[J]. ISRAEL JOURNAL OF MATHEMATICS, 2020, 240 (02) : 821 - 835
[6] Proof of a generalization of the (B.2) supercongruence of Van Hamme through a q-microscope
Guo, Victor J. W.
[J]. ADVANCES IN APPLIED MATHEMATICS, 2020, 116
[7] Some New q-Congruences for Truncated Basic Hypergeometric Series: Even Powers
Guo, Victor J. W.
Schlosser, Michael J.
[J]. RESULTS IN MATHEMATICS, 2020, 75 (01)
[8] Common q-Analogues of Some Different Supercongruences
Guo, Victor J. W.
[J]. RESULTS IN MATHEMATICS, 2019, 74 (04)
[9] A q-microscope for supercongruences
Guo, Victor J. W.
Zudilin, Wadim
[J]. ADVANCES IN MATHEMATICS, 2019, 346 : 329 - 358
[10] q-Analogues of two Ramanujan-type formulas for 1/π
Guo, Victor J. W.
Liu, Ji-Cai
[J]. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2018, 24 (08) : 1368 - 1373

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