A FAMILY OF q-SUPERCONGRUENCES MODULO THE CUBE OF A CYCLOTOMIC POLYNOMIAL

VICTOR J. W. GUO; MICHAEL J. SCHLOSSER

doi:10.1017/S0004972721000630

Titel

A FAMILY OF q-SUPERCONGRUENCES MODULO THE CUBE OF A CYCLOTOMIC POLYNOMIAL

Autor*in

VICTOR J. W. GUO

School of Mathematics and Statistics, Huaiyin Normal University

MICHAEL J. SCHLOSSER

Fakultät für Mathematik, Universität Wien

Abstract

We establish a family of q-supercongruences modulo the cube of a cyclotomic polynomial for truncated basic hypergeometric series. This confirms a weaker form of a conjecture of the present authors. Our proof employs a very-well-poised Karlsson–Minton type summation due to Gasper, together with the ‘creative microscoping’ method introduced by the first author in recent joint work with Zudilin.

Stichwort

basic hypergeometric seriessupercongruencesq-congruencescyclotomic polynomialGasper’s summation

Objekt-Typ

journal article

Sprache

Englisch [eng]

Persistent identifier

phaidra.univie.ac.at/o:1581256

DOI

10.1017/S0004972721000630

Erschienen in

Titel