Period polynomials, derivatives of L-functions, and zerosof polynomials

Diamantis, Nikolaos; Rolen, Larry

Abstract

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.

Citation

Diamantis, N., & Rolen, L. (2018). Period polynomials, derivatives of L-functions, and zerosof polynomials. Research in the Mathematical Sciences, 5, Article 9. https://doi.org/10.1007/s40687-018-0126-4

• Journal Article Type: Article
• Acceptance Date: Dec 21, 2017
• Online Publication Date: Feb 6, 2018
• Publication Date: Feb 6, 2018
• Deposit Date: Jan 19, 2018
• Publicly Available Date: Aug 16, 2018
• Journal: Research in the Mathematical Sciences
• Electronic ISSN: 2197-9847
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 5
• Article Number: 9
• DOI: https://doi.org/10.1007/s40687-018-0126-4
• Public URL: https://nottingham-repository.worktribe.com/output/901491
• Publisher URL: https://link.springer.com/article/10.1007/s40687-018-0126-4
• Contract Date: Aug 16, 2018