Regularized inner products and errors of modularity

Bringmann, Kathrin and Diamantis, Nikolaos and Ehlen, Stephan (2016) Regularized inner products and errors of modularity. International Mathematics Research Notices . ISSN 1687-0247

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Abstract

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.

Item Type: Article
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.com/imrn/article-lookup/doi/10.1093/imrn/rnw225
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1093/imrn/rnw225
Depositing User: Diamantis, Dr Nikolaos
Date Deposited: 06 Mar 2017 09:15
Last Modified: 03 Nov 2017 12:48
URI: http://eprints.nottingham.ac.uk/id/eprint/41010

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