Sign changes in short intervals of coefficients of spinor zeta function of a Siegel cusp form of genus 2

TL;DR

This paper establishes a Voronoi formula for the spinor zeta function of a genus 2 Siegel cusp form and uses it to analyze sign changes of its coefficients in short intervals.

Contribution

It introduces a Voronoi formula for the spinor zeta function of genus 2 Siegel cusp forms and applies it to study coefficient sign changes.

Findings

Quantitative results on positive and negative coefficient counts in short intervals

Demonstrates sign change behavior of coefficients in specific intervals

Provides a new analytical tool for studying Siegel cusp form coefficients

Abstract

In this paper, we establish a Voronoi formula for the spinor zeta function of a Siegel cusp form of genus 2. We deduce from this formula quantitative results on the number of its positive (resp. negative) coefficients in some short intervals.