Locally harmonic Maass forms and periods of meromorphic modular forms
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- by Steffen Löbrich and Markus Schwagenscheidt PDF
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Abstract:
We investigate a new family of locally harmonic Maass forms which correspond to periods of modular forms. They transform like negative weight modular forms and are harmonic apart from jump singularities along infinite geodesics. Our main result is an explicit splitting of the new locally harmonic Maass forms into a harmonic part and a locally polynomial part that captures the jump singularities. As an application, we obtain finite rational formulas for suitable linear combinations of periods of meromorphic modular forms associated to positive definite binary quadratic forms.References
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Additional Information
- Steffen Löbrich
- Affiliation: Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Science Park 105-107, 1098 XG Amsterdam, The Netherlands
- Email: s.loebrich@uva.nl
- Markus Schwagenscheidt
- Affiliation: Department of Mathematics, ETH Zürich, Rämistrasse 101, CH-8092 Zürich, Switzerland
- MR Author ID: 1094068
- ORCID: 0000-0002-8214-3106
- Email: mschwagen@ethz.ch
- Received by editor(s): January 16, 2021
- Received by editor(s) in revised form: May 11, 2021
- Published electronically: October 28, 2021
- Additional Notes: The work of the first author was supported by ERC starting grant H2020 ERC StG #640159. The second author was supported by SNF project 200021_185014
- © Copyright 2021 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 375 (2022), 501-524
- MSC (2020): Primary 11F11, 11F37, 11F67
- DOI: https://doi.org/10.1090/tran/8528
- MathSciNet review: 4358674