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.