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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Vydáno v:Resultate der Mathematik Ročník 75; číslo 1; s. 1
Hlavní autoři: Guo, Victor J. W., Schlosser, Michael J.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cham Springer International Publishing 01.03.2020
Témata:
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
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Popis
Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1422-6383
1420-9012
1420-9012
DOI:10.1007/s00025-019-1126-4