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

摘要

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.