
Open access
Date
2015-06Type
- Journal Article
Citations
Cited 20 times in
Web of Science
Cited 18 times in
Scopus
ETH Bibliography
yes
Altmetrics
Abstract
In this paper, we use regularized theta liftings to construct weak Maass formsof weight 1/2 as lifts of weak Maass forms of weight 0. As a special case we give a new proofof 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 tosettle the open question of a geometric interpretation for periods of j along infinite geodesics inthe 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 forboth the CM points and the geodesic cycles, which is of independent interest. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000078070Publication status
publishedExternal links
Journal / series
Journal für die reine und angewandte MathematikVolume
Pages / Article No.
Publisher
De GruyterOrganisational unit
08799 - Imamoglu, Oezlem (Tit.-Prof.)
Notes
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.More
Show all metadata
Citations
Cited 20 times in
Web of Science
Cited 18 times in
Scopus
ETH Bibliography
yes
Altmetrics