Riemann hypothesis for period polynomials attached to the derivatives of L-functions of cusp forms for G(0)(N)

Abstract

We prove the Riemann hypothesis for the period polynomials attached to the first derivatives of L-functions of newforms integral & nbsp;is an element of & nbsp;S-k & nbsp;(gamma(0)(N)) for all but finitely many pairs (k, N) of weight k and level N, as an extension of the results by Jin, Ma, Ono and Soundararajan [8] and by Diamantis and Rolen [4,5]. (C)& nbsp;2021 Elsevier Inc. All rights reserved.