Some variations of a "divergent" Ramanujan-type q-supercongruence

2020/04/20 by Guo, Victor J. W.
#05A10 #05A30 #11B65 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2004.10526

Abstract

Using the q-Wilf--Zeilberger method and a q-analogue of a "divergent" Ramanujan-type supercongruence, we give several q-supercongruences modulo the fourth power of a cyclotomic polynomial. One of them is a q-analogue of a supercongruence recently proved by Wang: for any prime p>3, ∑_k=0^p-1 (3k-1)(((1)/(2))_k (-(1)/(2))_k² )/(k!³)4^k≡ p-2p³ \pmodp⁴, where (a)_k=a(a+1)⋯ (a+k-1) is the Pochhammer symbol.

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