Traces of CM values of modular functions

Bruinier, J.; Funke, J.

doi:10.1515/crelle.2006.034

Traces of CM values of modular functions

Bruinier, J.; Funke, J.

Authors

J. Bruinier

Professor Jens Funke jens.funke@durham.ac.uk
Professor

Abstract

Zagier proved that the traces of singular moduli, i.e., the sums of the values of the classical j-invariant over quadratic irrationalities, are the Fourier coefficients of a modular form of weight 3/2 with poles at the cusps. Using the theta correspondence, we generalize this result to traces of CM values of (weakly holomorphic) modular functions on modular curves of arbitrary genus. We also study the theta lift for the weight 0 Eisenstein series for SL2() and realize a certain generating series of arithmetic intersection numbers as the derivative of Zagier's Eisenstein series of weight 3/2. This recovers a result of Kudla, Rapoport and Yang.

Citation

Bruinier, J., & Funke, J. (2006). Traces of CM values of modular functions. Journal für die reine und angewandte Mathematik, 594, 1-33. https://doi.org/10.1515/crelle.2006.034

Journal Article Type	Article
Publication Date	May 1, 2006
Deposit Date	Feb 16, 2009
Publicly Available Date	Mar 18, 2014
Journal	Journal für die reine und angewandte Mathematik
Print ISSN	0075-4102
Electronic ISSN	1435-5345
Publisher	De Gruyter
Peer Reviewed	Peer Reviewed
Volume	594
Pages	1-33
DOI	https://doi.org/10.1515/crelle.2006.034