Explicit inner product formulas and Bessel period formulas for HST lifts

TL;DR

This paper derives explicit formulas for inner products and Bessel periods of theta series on GSp(4), enabling non-vanishing results and criteria for theta series modulo primes, advancing understanding of automorphic forms.

Contribution

It provides explicit formulas for inner products and Bessel periods of theta series on GSp(4), which were previously not explicitly known.

Findings

Non-vanishing of theta series of small weights

Non-vanishing criteria modulo primes

Explicit inner product and Bessel period formulas

Abstract

We explicitly give an inner product formula and a Bessel period formula for theta series on GSp(4), which was studied by Harris, Soudry and Taylor. As a consequence, we prove a non-vanishing of the theta series of small weights and we give a criterion for the non-vanishing of the theta series modulo a prime.