Regularized inner products and errors of modularity
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. T...
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| Format: | Article |
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Oxford University Press
2017
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| Online Access: | https://eprints.nottingham.ac.uk/41010/ |
| _version_ | 1848796177134256128 |
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| author | Bringmann, Kathrin Diamantis, Nikolaos Ehlen, Stephan |
| author_facet | Bringmann, Kathrin Diamantis, Nikolaos Ehlen, Stephan |
| author_sort | Bringmann, Kathrin |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:43:50Z |
| format | Article |
| id | nottingham-41010 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:43:50Z |
| publishDate | 2017 |
| publisher | Oxford University Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-410102020-05-04T19:20:20Z https://eprints.nottingham.ac.uk/41010/ Regularized inner products and errors of modularity Bringmann, Kathrin Diamantis, Nikolaos Ehlen, Stephan 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. Oxford University Press 2017-12-01 Article PeerReviewed Bringmann, Kathrin, Diamantis, Nikolaos and Ehlen, Stephan (2017) Regularized inner products and errors of modularity. International Mathematics Research Notices, 2017 (24). pp. 7420-7458. ISSN 1687-0247 https://academic.oup.com/imrn/article-lookup/doi/10.1093/imrn/rnw225 doi:10.1093/imrn/rnw225 doi:10.1093/imrn/rnw225 |
| spellingShingle | Bringmann, Kathrin Diamantis, Nikolaos Ehlen, Stephan Regularized inner products and errors of modularity |
| title | Regularized inner products and errors of modularity |
| title_full | Regularized inner products and errors of modularity |
| title_fullStr | Regularized inner products and errors of modularity |
| title_full_unstemmed | Regularized inner products and errors of modularity |
| title_short | Regularized inner products and errors of modularity |
| title_sort | regularized inner products and errors of modularity |
| url | https://eprints.nottingham.ac.uk/41010/ https://eprints.nottingham.ac.uk/41010/ https://eprints.nottingham.ac.uk/41010/ |