On the zeros of period functions associated to the Eisenstein series for Gamma(+)(0) (N)

Abstract

We consider the period functions associated to the Eisenstein series for the Fricke group Gamma(+)(0) (N), the odd parts of the period functions and certain polynomials obtained from the period functions for Gamma(+)(0) (N), and we prove that all zeros of each of them lie on the circle |z| = 1/root N by applying the properties of a self-inversive polynomial. In particular, our result proves Berndt and Straub's suggested problem. (c) 2021 Elsevier Inc. All rights reserved.