Bessel periods and the non-vanishing of Yoshida lifts modulo a prime

TL;DR

This paper constructs explicit Yoshida lifts, derives a Bessel period formula, and proves their non-vanishing modulo a prime, providing new insights into the arithmetic properties of these automorphic forms.

Contribution

It offers an explicit construction of vector-valued Yoshida lifts and a novel proof of their non-vanishing modulo a prime, advancing understanding of automorphic forms.

Findings

Explicit construction of Yoshida lifts

Formula for Bessel periods of Yoshida lifts

Proof of non-vanishing modulo a prime

Abstract

We give an explicit construction of vector-valued Yoshida lifts and derive a formula of the Bessel periods of Yoshida lifts, by which we prove the non-vanishing modulo a prime of Yoshida lifts attached to a pair of elliptic modular newforms. As a consequence, we obtain a new proof of the non-vanishing of Yoshida lifts.