Root Number Equidistribution for Self-Dual Automorphic Representations on $G{L}_N$

Rahul Dalal, Mathilde Gerbelli-Gauthier

Let $F$ be a totally real field. We study the root numbers $\epsilon (1/2,\pi )$ of self-dual cuspidal automorphic representations $\pi$ of ${\mathrm{GL}}_{2N}/F$ with conductor $\mathfrak{n}$ an…