Next Article in Journal
One-Dimensional Nonlinear Stefan Problems in Storm’s Materials
Previous Article in Journal
Effective Congruences for Mock Theta Functions
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
Download PDF [185 KB, uploaded 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 singular moduli; sign change; circle method
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Share & Cite This Article

Export to BibTeX |
EndNote


MDPI and ACS Style

Choi, D.; Kim, B.; Lim, S. Sign-Periodicity of Traces of Singular Moduli. Mathematics 2013, 1, 111-118.

View more citation formats

Article Metrics

Comments

Citing Articles

[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert