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

ABSTRACT: 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.

SUBMITTER: Guo VJW

PROVIDER: S-EPMC7067271 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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

Guo Victor J W VJW Schlosser Michael J MJ

Results in mathematics 20191128 1

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 powe ...[more]

PMID: 32214886

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