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Congruences Involving Hecke-Rogers Type Series and Modular Forms

Congruences Involving Hecke-Rogers Type Series and Modular Forms

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,pnf2,n(mod p2)  when  p1(mod 4), where
η(τ)=q124Πn=1(1qn),
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.

Author Details

Guo-Shuai Mao Email

Yan Liu Email