Explicit inner product formulas and Bessel period formulas for HST lifts

Abstract

We explicitly give an inner product formula and a Bessel period formula for theta series on ${\mathrm{GSp}}_4$, which was studied by Harris, Soudry, and Taylor. As a consequence, we prove a nonvanishing of the theta series of small weights and we give a criterion for the nonvanishing of the theta series modulo a prime.