Year: 2023
Author: Guo-Shuai Mao, Yan Liu
Journal of Mathematical Study, Vol. 56 (2023), Iss. 2 : pp. 147–155
Abstract
In this paper, we prove two supercongruences of Hecke-Rogers type series
and Modular forms conjectured by Chan, Cooper and Sica, such as, if
z2=∞∑m=−∞∞∑n=−∞qm2+n2,x2=η12(2τ)z62
and
z2=∞∑n=0f2,nxn2,
then
f2,pn≡f2,n(mod p2) when p≡1(mod 4), where
η(τ)=q124Π∞n=1(1−qn),
and q=exp(2πiτ) with Im(τ)>0.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v56n2.23.03
Journal of Mathematical Study, Vol. 56 (2023), Iss. 2 : pp. 147–155
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: Supercongruences modular forms Hecke-Rogers type series p-adic Gamma function.