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

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...

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Bibliographic Details
Published in:Resultate der Mathematik Vol. 75; no. 1; p. 1
Main Authors: Guo, Victor J. W., Schlosser, Michael J.
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.03.2020
Subjects:
Mathematics
Mathematics and Statistics
Primary 33D15
Andrews’ transformation
supercongruences
cyclotomic polynomial
11B65
Basic hypergeometric series
congruences
Secondary 11A07
q-congruences
ISSN:1422-6383, 1420-9012, 1420-9012
Online Access:Get full text
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Summary: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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ISSN:1422-6383
1420-9012
1420-9012
DOI:10.1007/s00025-019-1126-4