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

被引：0
作者：
Victor J. W. Guo
Michael J. Schlosser
机构：
[1] Huaiyin Normal University,School of Mathematics and Statistics
[2] Universität Wien,Fakultät für Mathematik
来源：
Results in Mathematics | 2020年 / 75卷
关键词：
Basic hypergeometric series; supercongruences; -congruences; cyclotomic polynomial; Andrews’ transformation; Primary 33D15; Secondary 11A07; 11B65;
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摘要：
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.
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  • [1] Calkin NJ(1998)Factors of sums of powers of binomial coefficients Acta Arith. 86 17-26
  • [2] Gorodetsky O(2019)-Congruences, with applications to supercongruences and the cyclic sieving phenomenon Int. J. Number Theory 15 1919-1968
  • [3] Guo VJW(2018)A J. Math. Anal. Appl. 458 590-600
  • [4] Guo VJW(2019)-analogue of a Ramanujan-type supercongruence involving central binomial coefficients Int. J. Number Theory 15 29-36
  • [5] Guo VJW(2019)A Results Math. 74 131-350
  • [6] Guo VJW(2019)-analogue of the (I.2) supercongruence of Van Hamme J. Differ. Equ. Appl. 25 342-393
  • [7] Guo VJW(2019)Common Acta Arith. 190 381-31
  • [8] Guo VJW(2007)-analogues of some different supercongruences Acta Arith. 127 17-1373
  • [9] Jouhet F(2018)A J. Differ. Equ. Appl. 24 1368-368
  • [10] Zeng J(2017)-analogue of a curious supercongruence of Guillera and Zudilin J. Number Theory 174 358-929
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