Traces of singular moduli of arbitrary level modular functions

Dohoon Choi, Daeyeol Jeon, Soon Yi Kang, Chang Heon Kim

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Generalizing Zagier's work, Bruinier and Funke recently proved that for modular curves of arbitrary genus, the generating series for the traces of the CM values of a weakly holomorphic modular function is the holomorphic part of a harmonic weak Maass form of weight 3/2. The present article shows that by adding a suitable linear combination of weight 3/2 Eisenstein series, one can always obtain a generating series that is weakly holomorphic. In particular, the modular traces of a Hauptmodul on Γ*0(4) are found to be either Fourier coefficients of a weakly holomorphic modular form of weight 3/2 or constantmultiples of class numbers. As an application, we obtain congruence properties for the traces of singular moduli of a weakly holomorphic modular function of arbitrary level.

Original languageEnglish
Article numberrnm110
JournalInternational Mathematics Research Notices
Volume2007
DOIs
Publication statusPublished - 2007 Dec 1
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Traces of singular moduli of arbitrary level modular functions'. Together they form a unique fingerprint.

  • Cite this