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.