Mock period functions, sesquiharmonic Maass forms, and non-critical values of L-functions
We introduce a new technique of completion for 1-cohomology which parallels the corresponding technique in the theory of mock modular forms. This technique is applied in the context of non-critical values of L-functions of GL(2) cusp forms. We prove that a generating series of non-critical values ca...
| Main Authors: | , , |
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| Format: | Article |
| Published: |
Elsevier
2013
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| Online Access: | https://eprints.nottingham.ac.uk/2765/ |
| _version_ | 1848790870212476928 |
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| author | Bringmann, Kathrin Diamantis, Nikolaos Raum, Martin |
| author_facet | Bringmann, Kathrin Diamantis, Nikolaos Raum, Martin |
| author_sort | Bringmann, Kathrin |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We introduce a new technique of completion for 1-cohomology which parallels the corresponding technique in the theory of mock modular forms. This technique is applied in the context of non-critical values of L-functions of GL(2) cusp forms. We prove that a generating series of non-critical values can be interpreted as a mock period function we
define in analogy with period polynomials. Further, we prove that non-critical values can be encoded into a sesquiharmonic Maass form. Finally, we formulate and prove an Eichler-Shimura-type isomorphism for the space of mock period functions. |
| first_indexed | 2025-11-14T18:19:29Z |
| format | Article |
| id | nottingham-2765 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:19:29Z |
| publishDate | 2013 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-27652020-05-04T20:19:51Z https://eprints.nottingham.ac.uk/2765/ Mock period functions, sesquiharmonic Maass forms, and non-critical values of L-functions Bringmann, Kathrin Diamantis, Nikolaos Raum, Martin We introduce a new technique of completion for 1-cohomology which parallels the corresponding technique in the theory of mock modular forms. This technique is applied in the context of non-critical values of L-functions of GL(2) cusp forms. We prove that a generating series of non-critical values can be interpreted as a mock period function we define in analogy with period polynomials. Further, we prove that non-critical values can be encoded into a sesquiharmonic Maass form. Finally, we formulate and prove an Eichler-Shimura-type isomorphism for the space of mock period functions. Elsevier 2013 Article PeerReviewed Bringmann, Kathrin, Diamantis, Nikolaos and Raum, Martin (2013) Mock period functions, sesquiharmonic Maass forms, and non-critical values of L-functions. Advances in Mathematics, 233 (1). pp. 115-134. ISSN 0001-8708 http://dx.doi.org/10.1016/j.aim.2012.09.025 doi:10.1016/j.aim.2012.09.025 doi:10.1016/j.aim.2012.09.025 |
| spellingShingle | Bringmann, Kathrin Diamantis, Nikolaos Raum, Martin Mock period functions, sesquiharmonic Maass forms, and non-critical values of L-functions |
| title | Mock period functions, sesquiharmonic Maass forms, and non-critical values of L-functions |
| title_full | Mock period functions, sesquiharmonic Maass forms, and non-critical values of L-functions |
| title_fullStr | Mock period functions, sesquiharmonic Maass forms, and non-critical values of L-functions |
| title_full_unstemmed | Mock period functions, sesquiharmonic Maass forms, and non-critical values of L-functions |
| title_short | Mock period functions, sesquiharmonic Maass forms, and non-critical values of L-functions |
| title_sort | mock period functions, sesquiharmonic maass forms, and non-critical values of l-functions |
| url | https://eprints.nottingham.ac.uk/2765/ https://eprints.nottingham.ac.uk/2765/ https://eprints.nottingham.ac.uk/2765/ |