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Regularized inner products and errors of modularity

Bringmann, Kathrin; Diamantis, Nikolaos; Ehlen, Stephan

Authors

Kathrin Bringmann

Stephan Ehlen



Abstract

© The Author(s) 2016. We develop a regularization for Petersson inner products of arbitrary weakly holomorphic modular forms, generalizing several known regularizations. As one application, we extend work of Duke, Imamoglu, and Toth on regularized inner products of weakly holomorphic modular forms of weights 0 and 3/2. These regularized inner products can be evaluated in terms of the coefficients of holomorphic parts of harmonic Maass forms of dual weights. Moreover, we study the errors of modularity of the holomorphic parts of such a harmonic Maass forms and show that they induce cocyles in the first parabolic cohomology group introduced by Bruggeman, Choie, and the second author. This provides explicit representatives of the cohomology classes constructed abstractly and in a very general setting in their work.

Journal Article Type Article
Publication Date Dec 1, 2017
Journal International Mathematics Research Notices
Print ISSN 1073-7928
Electronic ISSN 1687-0247
Publisher Oxford University Press
Peer Reviewed Peer Reviewed
Volume 2017
Issue 24
Pages 7420-7458
APA6 Citation Bringmann, K., Diamantis, N., & Ehlen, S. (2017). Regularized inner products and errors of modularity. International Mathematics Research Notices, 2017(24), 7420-7458. https://doi.org/10.1093/imrn/rnw225
DOI https://doi.org/10.1093/imrn/rnw225
Publisher URL https://academic.oup.com/imrn/article-lookup/doi/10.1093/imrn/rnw225
Related Public URLs https://arxiv.org/abs/1603.03056v2
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information This is a pre-copyedited, author-produced version of an article accepted for publication in International Mathematics Research Notices following peer review. The version of record Kathrin Bringmann, Nikolaos Diamantis, Stephan Ehlen; Regularized Inner Products and Errors of Modularity. Int Math Res Notices 2016 is available online at: https://academic.oup.co...doi/10.1093/imrn/rnw225

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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