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Regularized theta liftings and periods of modular functions.

Bruinier, Jan and Funke, Jens and Imamoḡlu, Özlem (2015) 'Regularized theta liftings and periods of modular functions.', Journal für die reine und angewandte Mathematik. = Crelles journal., 2015 (703). pp. 43-93.

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.

Item Type:Article
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1515/crelle-2013-0035
Publisher statement:The final publication is available at www.degruyter.com
Date accepted:13 March 2013
Date deposited:07 May 2014
Date of first online publication:18 June 2013
Date first made open access:No date available

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