On the global Gross-Prasad conjecture for Yoshida liftings

TL;DR

This paper investigates the restriction of Yoshida liftings, a special type of Siegel modular form, to embedded products of half planes, linking Petersson products to central L-values and addressing the Gross-Prasad conjecture.

Contribution

It provides an explicit formula relating Petersson products of Yoshida liftings to central L-values, advancing understanding of automorphic restrictions and the Gross-Prasad conjecture.

Findings

Explicit expression for Petersson product in terms of L-values

Connection established between Yoshida liftings and Gross-Prasad conjecture

Results support conjectural relationships in automorphic representation restrictions

Abstract

We restrict a Siegel modular cusp form of degree 2 and square free level that is a Yoshida lifting (a lifting from the orthogonal group of a definite quaternion algebra) to the embedded product of two half planes and compute the Petersson product against the product of two elliptic cuspidal Hecke eigenforms. The square of this integral can be explicitly expressed in terms of the central critical value of an L-function attached to the situation. The result is related to a conjecture of Gross and Prasad about restrictions of automorphic representations of special orthogonal groups.