A family of q-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial

We prove a two-parameter family of q -hypergeometric congruences modulo the fourth power of a cyclotomic polynomial. Crucial ingredients in our proof are George Andrews’ multiseries extension of the Watson transformation, and a Karlsson—Minton-type summation for very-well-poised basic hypergeometric...

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Bibliographic Details
Published inIsrael journal of mathematics Vol. 240; no. 2; pp. 821 - 835
Main Authors Guo, Victor J. W., Schlosser, Michael J.
Format Journal Article
LanguageEnglish
Published Jerusalem The Hebrew University Magnes Press 01.10.2020
Subjects
Algebra
Analysis
Applications of Mathematics
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
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Summary:We prove a two-parameter family of q -hypergeometric congruences modulo the fourth power of a cyclotomic polynomial. Crucial ingredients in our proof are George Andrews’ multiseries extension of the Watson transformation, and a Karlsson—Minton-type summation for very-well-poised basic hypergeometric series due to George Gasper. The new family of q -congruences is then used to prove two conjectures posed earlier by the authors.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-020-2081-1