Divisibilities and Congruences Identities on Traces of Singular Moduli
Received:November 09, 2017  Revised:July 06, 2018
Key Word: traces of singular moduli   divisibilities   congruences   Hecke operators  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.61402335), the Natural Science Foundation of Shaanxi Province (Grant No.2016JM1004), the Scientific Research Program Funded by Shaanxi Provincial Education Department (Grant No.17JK0266) and the Natural Science Foundation of Weinan Normal University (Grant Nos.17ZRRC01; 17YKS09).
Author NameAffiliation
Bin CHEN Department of Mathematics and Physics, Weinan Normal University, Shaanxi 714099, P.R. China 
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      Zagier found that traces of singular moduli are the Fourier coefficients of certain modular forms of weight $3/2$. As a result, formulas and congruences of these traces are obtained in various situations. Recently, Ahlgen proved a uniform relationship for traces of singular moduli by using the relationship of modular forms with the action of Hecke operators. On the basis of these results, we get some interesting divisibilities and congruences identities on traces of singular moduli and Hurwitz-Kronecker class number.
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