The functional equation for the twisted spinor L-series of genus 2

TL;DR

This paper proves the functional equation for the twisted spinor L-series of genus 2 Siegel eigenforms, extending to Rankin convolutions, with a key non-vanishing Fourier-Jacobi coefficient result.

Contribution

It establishes the functional equation for the twisted spinor L-series of genus 2 Siegel eigenforms, generalizing to Rankin convolutions with a new non-vanishing result.

Findings

Proved the functional equation for the twisted spinor L-series.

Extended the functional equation to Rankin convolutions.

Established a non-vanishing result for Fourier-Jacobi coefficients.

Abstract

We prove the functional equation for the twisted spinor L-series of a cuspidal, holomorphic Siegel eigenform for the full modular group of genus 2. It follows from a more general functional equation, valid for Rankin convolutions of paramodular cuspforms. A non-vanishing result for Fourier-Jacabi coefficients of the eigenforms in question is the central pillar of the deduction of the former from the latter functional equation.