Low-lying zeros for L-functions associated to Hilbert modular forms of large level

TL;DR

This paper investigates the distribution of low-lying zeros in families of Hilbert modular forms with large level, revealing their statistical behavior aligns with orthogonal random matrix ensembles.

Contribution

It provides the first detailed analysis of 1-level density for Hilbert modular forms, confirming their zeros follow orthogonal symmetry.

Findings

Zeros follow orthogonal symmetry

Matches predictions from random matrix theory

Advances understanding of L-functions in number theory

Abstract

We determine the 1-level density of families of Hilbert modular forms, and show the answer agrees only with orthogonal random matrix ensembles.