An explicit bound for the first sign change of the Fourier coefficients

TL;DR

This paper establishes an explicit upper bound for the first sign change in the Fourier coefficients of non-zero Siegel cusp forms of even weight across any genus g ≥ 2, advancing understanding of their oscillatory behavior.

Contribution

It provides the first explicit bound for the initial sign change of Fourier coefficients of Siegel cusp forms of arbitrary genus g ≥ 2.

Findings

Derived an explicit upper bound for the first sign change.

Applicable to Siegel cusp forms of any genus g ≥ 2.

Enhances understanding of Fourier coefficient oscillations.

Abstract

We give an explicit upper bound for the first sign change of the Fourier coefficients of an arbitrary non-zero Siegel cusp form $F$ of even integral weight on the Siegel modular group of arbitrary genus $ g\geq 2 $.