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Mathematics 2013, 1(4), 111-118; doi:10.3390/math1040111
Article

Sign-Periodicity of Traces of Singular Moduli

1
,
2
 and
3,*
1 School of Liberal Arts and Sciences, Korea Aerospace University, 200-1, Hwajeon-dong, Goyang, Gyeonggi 412-791, Korea 2 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 3 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 / Revised: 9 September 2013 / Accepted: 8 October 2013 / Published: 15 October 2013
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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 singular moduli; sign change; circle method
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Choi, D.; Kim, B.; Lim, S. Sign-Periodicity of Traces of Singular Moduli. Mathematics 2013, 1, 111-118.

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