Period polynomials, derivatives of $L$-functions, and zeros of polynomials

Nikolaos Diamantis; Larry Rolen

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arXiv · 1707.04814

Period polynomials, derivatives of $L$-functions, and zeros of polynomials

Nikolaos Diamantis·Larry Rolen

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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.

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Nikolaos Diamantis, Larry Rolen. 2017-07-16. Period polynomials, derivatives of $L$-functions, and zeros of polynomials. https://arxiv.org/abs/1707.04814

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