Period polynomials, derivatives of L-functions, and zeros of polynomials
Period polynomials have long been fruitful tools for the study of values of L-functions in the context of major outstanding conjectures. In this paper, we survey some facets of this study from the perspective of Eichler cohomology. We discuss ways to incorporate non-cuspidal modular forms and values...
| Main Authors: | , |
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| Format: | Article |
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Springer
2017
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| Online Access: | https://eprints.nottingham.ac.uk/49203/ |
| _version_ | 1848797944773345280 |
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| author | Diamantis, Nikolaos Rolen, Larry |
| author_facet | Diamantis, Nikolaos Rolen, Larry |
| author_sort | Diamantis, Nikolaos |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Period polynomials have long been fruitful tools for the study of values of L-functions in the context of major outstanding conjectures. In this paper, we survey some facets of this study from the perspective of Eichler cohomology. We discuss ways to incorporate non-cuspidal modular forms and values of derivatives of L-functions into the same framework. We further review investigations of the location of zeros of the period polynomial as well as of its analogue for L-derivatives. |
| first_indexed | 2025-11-14T20:11:56Z |
| format | Article |
| id | nottingham-49203 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:11:56Z |
| publishDate | 2017 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-492032020-05-04T19:23:46Z https://eprints.nottingham.ac.uk/49203/ Period polynomials, derivatives of L-functions, and zeros of polynomials Diamantis, Nikolaos Rolen, Larry Period polynomials have long been fruitful tools for the study of values of L-functions in the context of major outstanding conjectures. In this paper, we survey some facets of this study from the perspective of Eichler cohomology. We discuss ways to incorporate non-cuspidal modular forms and values of derivatives of L-functions into the same framework. We further review investigations of the location of zeros of the period polynomial as well as of its analogue for L-derivatives. Springer 2017-12-21 Article PeerReviewed Diamantis, Nikolaos and Rolen, Larry (2017) Period polynomials, derivatives of L-functions, and zeros of polynomials. Research in the Mathematical Sciences . ISSN 2197-9847 (In Press) https://doi.org/10.1007/s40687-018-126-4 doi:10.1007/s40687-018-126-4 doi:10.1007/s40687-018-126-4 |
| spellingShingle | Diamantis, Nikolaos Rolen, Larry Period polynomials, derivatives of L-functions, and zeros of polynomials |
| title | Period polynomials, derivatives of L-functions, and zeros
of polynomials |
| title_full | Period polynomials, derivatives of L-functions, and zeros
of polynomials |
| title_fullStr | Period polynomials, derivatives of L-functions, and zeros
of polynomials |
| title_full_unstemmed | Period polynomials, derivatives of L-functions, and zeros
of polynomials |
| title_short | Period polynomials, derivatives of L-functions, and zeros
of polynomials |
| title_sort | period polynomials, derivatives of l-functions, and zeros
of polynomials |
| url | https://eprints.nottingham.ac.uk/49203/ https://eprints.nottingham.ac.uk/49203/ https://eprints.nottingham.ac.uk/49203/ |