Zeros of theta functions associated with even unimodular lattices

Roei Raveh

公開日: 2025/9/7

Abstract

We study the zeros of the theta functions of the lattices $\Gamma_{8k}$, a family of even unimodular lattices generalizing the $\mathsf{E}_{8}$ lattice. We show that the zeros of $\Theta_{\Gamma_{8k}}$ all lie on the line $\Re z =\frac{1}{2}$ in the fundamental domain and compute their height and limit distribution.

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