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...
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| Format: | Article |
| Language: | English |
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Springer
2018
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| Online Access: | https://eprints.nottingham.ac.uk/51363/ |
| _version_ | 1848798479960244224 |
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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 | 2025-11-14T20:20:26Z |
| format | Article |
| id | nottingham-51363 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:20:26Z |
| publishDate | 2018 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-513632019-02-06T04:30:15Z https://eprints.nottingham.ac.uk/51363/ 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 2018-03-30 Article PeerReviewed application/pdf en https://eprints.nottingham.ac.uk/51363/1/PpDerRoots812.pdf Diamantis, Nikolaos and Rolen, Larry (2018) Period polynomials, derivatives of L-functions, and zeros of polynomials. Research in the Mathematical Sciences, 5 . p. 9. ISSN 2197-9847 https://link.springer.com/article/10.1007%2Fs40687-018-0126-4 doi:10.1007/s40687-018-0126-4 doi:10.1007/s40687-018-0126-4 |
| 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/51363/ https://eprints.nottingham.ac.uk/51363/ https://eprints.nottingham.ac.uk/51363/ |