On the rationality of cycle integrals of meromorphic modular forms

We derive finite rational formulas for the traces of cycle integrals of certain meromorphic modular forms. Moreover, we prove the modularity of a completion of the generating function of such traces. The theoretical framework for these results is an extension of the Shintani theta lift to meromorphi...

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Bibliographic Details
Published inMathematische annalen Vol. 376; no. 1-2; pp. 243 - 266
Main Authors Alfes-Neumann, Claudia, Bringmann, Kathrin, Schwagenscheidt, Markus
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2020
Springer Nature B.V
Subjects
Analytic functions
Cycle ratio
Integrals
Mathematics
Mathematics and Statistics
Modularity
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Summary:We derive finite rational formulas for the traces of cycle integrals of certain meromorphic modular forms. Moreover, we prove the modularity of a completion of the generating function of such traces. The theoretical framework for these results is an extension of the Shintani theta lift to meromorphic modular forms of positive even weight.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-019-01914-4