Skip to main content

Research Repository

Advanced Search

Regularized theta liftings and periods of modular functions

Bruinier, Jan; Funke, Jens; Imamoglu, Ozlem

Regularized theta liftings and periods of modular functions Thumbnail


Authors

Jan Bruinier

Ozlem Imamoglu



Abstract

In this paper, we use regularized theta liftings to construct weak Maass forms of weight 1/2 as lifts of weak Maass forms of weight 0. As a special case we give a new proof of some of recent results of Duke, Toth and the third author on cycle integrals of the modular j-invariant and extend these to any congruence subgroup. Moreover, our methods allow us to settle the open question of a geometric interpretation for periods of j along infinite geodesics in the upper half plane. In particular, we give the `central value' of the (non-existent) `L-function' for j. The key to the proofs is the construction of a kind of simultaneous Green function for both the CM points and the geodesic cycles, which is of independent interest.

Citation

Bruinier, J., Funke, J., & Imamoglu, O. (2015). Regularized theta liftings and periods of modular functions. Journal für die reine und angewandte Mathematik, 2015(703), 43-93. https://doi.org/10.1515/crelle-2013-0035

Journal Article Type Article
Acceptance Date Mar 13, 2013
Online Publication Date Jun 18, 2013
Publication Date Jun 1, 2015
Deposit Date Mar 19, 2012
Publicly Available Date Mar 28, 2024
Journal Journal für die reine und angewandte Mathematik
Print ISSN 0075-4102
Electronic ISSN 1435-5345
Publisher De Gruyter
Peer Reviewed Peer Reviewed
Volume 2015
Issue 703
Pages 43-93
DOI https://doi.org/10.1515/crelle-2013-0035

Files

Published Journal Article (Advance online version) (594 Kb)
PDF

Copyright Statement
Advance online version The final publication is available at www.degruyter.com




You might also like



Downloadable Citations