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Sign-Periodicity of Traces of Singular Moduli
School of Liberal Arts and Sciences, Korea Aerospace University, 200-1, Hwajeon-dong, Goyang, Gyeonggi 412-791, Korea
School of Liberal Arts and Institute of Convergence Fundamental Studies, Seoul National University of Science and Technology, 172 Gongreung 2 dong, Nowongu, Seoul 139–743, Korea
School of Mathematics, Korea Institute for Advanced Study, Hoegiro 85, Dongdaemun-gu, Seoul 130-722, Korea
* Author to whom correspondence should be addressed.
Received: 9 August 2013; in revised form: 9 September 2013 / Accepted: 8 October 2013 / Published: 15 October 2013
Abstract: Zagier proved that the generating functions of traces of singular values of Jm(z) are weight 3/2 weakly holomorphic modular forms. In this paper we prove that there is the sign-periodicity of traces of singular values of Jm(z).
Keywords: singular moduli; sign change; circle method
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MDPI and ACS Style
Choi, D.; Kim, B.; Lim, S. Sign-Periodicity of Traces of Singular Moduli. Mathematics 2013, 1, 111-118.
Choi D, Kim B, Lim S. Sign-Periodicity of Traces of Singular Moduli. Mathematics. 2013; 1(4):111-118.
Choi, Dohoon; Kim, Byungchan; Lim, Subong. 2013. "Sign-Periodicity of Traces of Singular Moduli." Mathematics 1, no. 4: 111-118.