Congruences Involving Hecke-Rogers Type Series and Modular Forms  

作　　者：Guo-Shuai Mao Yan Liu 

机构地区：[1]Department of Mathematics,Nanjing University of Information Science and Technology,Nanjing 210044,China

出　　处：《Journal of Mathematical Study》2023年第2期147-155,共9页数学研究（英文）

基　　金：supported by the National Natural Science Foundation of China(Grant No.12001288);China Scholarship Council(Grant No.202008320187).

摘　　要：In this paper,we prove two supercongruences of Hecke-Rogers type series and Modular forms conjectured by Chan,Cooper and Sica,such as,if z_(2)∞∑m=-∞n=-∞,q^(m^(2+n^(2))),x_(2)=η^(12)(2ι)/_(2)^(6)and z_(2)=∞∑n=0f2,nxn2,then f_(2)pn≡f_(2)n(mod p^(2))when p≡1(mod 4),η(ι)=q1/21∞Пn=1(1-q^(n)),and q=exp(2πiτ)with Im(τ)>0.

关 键 词：Supercongruences mordular forms Hecke-Rogers type series p-adic Gamma function 

分 类 号：O15[理学—数学]