Equidistribution of signs for Hilbert modular forms of half-integral weight

TL;DR

This paper proves that the signs of Fourier coefficients of Hilbert modular forms of half-integral weight are evenly distributed, extending previous results from rational to totally real number fields using the Shimura correspondence.

Contribution

It generalizes the equidistribution of signs result to Hilbert modular forms over totally real fields, broadening the scope of previous work.

Findings

Signs of Fourier coefficients are equidistributed in specified subfamilies.

The result extends Inam and Wiese's work to totally real fields.

Uses Shimura correspondence to analyze Fourier coefficients.

Abstract

We prove an equidistribution of signs for the Fourier coefficients of Hilbert modular forms of half-integral weight. Our study focuses on certain subfamilies of coefficients that are accessible via the Shimura correspondence. This is a generalization of the result of Inam and Wiese to the setting of totally real number fields