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Medientyp:
E-Artikel
Titel:
Regularized theta liftings and periods of modular functions
Beteiligte:
Bruinier, Jan H.;
Funke, Jens;
Imamoḡlu, Özlem
Erschienen:
Walter de Gruyter GmbH, 2015
Erschienen in:Journal für die reine und angewandte Mathematik (Crelles Journal)
Sprache:
Englisch
DOI:
10.1515/crelle-2013-0035
ISSN:
0075-4102;
1435-5345
Entstehung:
Anmerkungen:
Beschreibung:
<jats:title>Abstract</jats:title>
<jats:p>
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 <jats:italic>j</jats:italic>-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 <jats:italic>j</jats:italic> along
infinite geodesics in the upper half plane. In particular, we give the
`central value' of the (non-existent) `<jats:italic>L</jats:italic>-function' for <jats:italic>j</jats:italic>. 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.
</jats:p>