On non-vanishing and sign changes of the Fourier coefficients of Hilbert cusp forms

TL;DR

This paper investigates the behavior of Fourier coefficients of Hilbert cusp forms, focusing on their simultaneous non-vanishing and sign changes, contributing to understanding their oscillatory properties.

Contribution

It provides new results on the simultaneous non-vanishing and sign change phenomena of Fourier coefficients of Hilbert cusp forms.

Findings

Established conditions for non-vanishing of Fourier coefficients.

Demonstrated the occurrence of sign changes in Fourier coefficients.

Provided insights into the oscillatory nature of Hilbert cusp forms.

Abstract

In this article, we study (simultaneous) non-vanishing, (simultaneous) sign changes of Fourier coefficients of (two) Hilbert cusp forms, respectively.