Zeros of newform Eisenstein series on Γ0(N)

Abstract

We examine the zeros of newform Eisenstein series E χ1,χ2,k (z) of weight k on Γ 0 (q 1 q 2 ), where χ 1 and χ 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.