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

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 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Research in the Mathematical Sciences Springer Journals

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

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Publisher
Springer International Publishing
Copyright
Copyright © 2018 by The Author(s)
Subject
Mathematics; Mathematics, general; Applications of Mathematics; Computational Mathematics and Numerical Analysis
eISSN
2197-9847
D.O.I.
10.1007/s40687-018-0126-4
Publisher site
See Article on Publisher Site

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.

Journal

Research in the Mathematical SciencesSpringer Journals

Published: Feb 6, 2018

References

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