| Divisibilities and Congruences Identities on Traces of Singular Moduli |
| Received:November 09, 2017 Revised:July 06, 2018 |
| Key Words:
traces of singular moduli divisibilities congruences Hecke operators
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| Fund Project: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). |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2018.06.002 |
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