Zeros of Newform Eisenstein Series on ${\Gamma }_0(N)$

Abstract

We examine the zeros of newform Eisenstein series $E_{{\chi }_1,{\chi }_2,k}(z)$ of weight $k$ on ${\Gamma }_0(q_1{q}_2)$, where ${\chi }_1$ and ${\chi }_2$ are primitive characters modulo $q_1$ and $q_2$, respectively. We determine the location and distribution of a significant fraction of the zeros of these Eisenstein series for $k$ sufficiently large.

18 pages, 3 attached figures