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

Surjeet Kaushik, Indian Institute of Technology Hyderabad
Narasimha Kumar, Indian Institute of Technology Hyderabad
Naomi Tanabe, Bowdoin College

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 (Arch Math (Basel) 101:331–339, 2013) to the setting of totally real number fields.