Zeros of even and odd period polynomials

Abstract

Let $f\in S_k({\Gamma }_0(N))$ be a newform, and let $r_f^{\pm }(X)$ denote its corresponding even and odd period polynomials. For sufficiently large level and weight, we show that the zeros of $r_f^{\pm }(X)$ all lie on the circle $|X|=\frac{1}{\sqrt{N}}$.

arXiv comment22 pages