q-Analogues of two Ramanujan-type supercongruences

被引：26
|
作者：
Liu, Yudong [1 ]
Wang, Xiaoxia [1 ]
机构：
[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2021年 / 502卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Basic hypergeometric series; Supercongruences; q-Congruences; q-Analogue; Cyclotomic polynomial; CONJECTURES;
D O I：
10.1016/j.jmaa.2021.125238
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we establish a new q-congruence with parameters modulo the fourth power of a cyclotomic polynomial from Watson's (8)phi(7) transformation. Taking parameters substitution in our new q-congruence, we present a q-analogue of the (D.2) supercongruenceof Van Hamme and several different q-analogues of He's supercongruence for p equivalent to 1(mod3). Finally, we propose a Dwork-type supercongruence conjecture on He's supercongruence. (C) 2021 Elsevier Inc. All rights reserved.
引用
收藏
页数：14
相关论文
共 50 条
  • [31] BARNES AND RAMANUJAN-TYPE INTEGRALS ON THE Q-LINEAR LATTICE
    RAHMAN, M
    SUSLOV, SK
    SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1994, 25 (03) : 1002 - 1022
  • [32] Two hypergeometric summation theorems and Ramanujan-type series
    Liu, Hongmei
    Qi, Shuhua
    Zhang, You
    INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2013, 24 (11) : 905 - 910
  • [33] ZEROS OF RAMANUJAN-TYPE POLYNOMIALS
    Maji, Bibekananda
    Sarkar, Tithi
    arXiv, 2023,
  • [34] Ramanujan-type continuous measures for biorthogonal q-rational functions
    Atakishiyev, NM
    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1996, 29 (02): : 329 - 338
  • [35] ON THE q-ANALOGUES FOR SOME KANTOROVICH TYPE LINEAR OPERATORS
    Aral, Nazlim Deniz
    Sevinc, Zeynep
    JOURNAL OF MATHEMATICAL INEQUALITIES, 2022, 16 (02): : 575 - 576
  • [36] On two kinds of q-analogues of generalized Stirling numbers
    Xu, Aimin
    Tang, Peipei
    RAMANUJAN JOURNAL, 2017, 43 (02): : 371 - 381
  • [37] On two kinds of q-analogues of generalized Stirling numbers
    Aimin Xu
    Peipei Tang
    The Ramanujan Journal, 2017, 43 : 371 - 381
  • [38] Two q-Analogues of Poly-Stirling Numbers
    Miceli, Brian K.
    JOURNAL OF INTEGER SEQUENCES, 2011, 14 (09)
  • [39] Recent Advances for Ramanujan Type Supercongruences
    Chisholm, Sarah
    Deines, Alyson
    Swisher, Holly
    WOMEN IN NUMBERS 2: RESEARCH DIRECTIONS IN NUMBER THEORY, 2013, 606 : 189 - 206
  • [40] Relations among Ramanujan-type congruences II: Ramanujan-type congruences in half-integral weights
    Raum, Martin
    FORUM MATHEMATICUM, 2023, 35 (03) : 615 - 646
12345