A relation between multiplicity one and Bocherer's conjecture

TL;DR

This paper demonstrates that a weaker version of Bocherer's conjecture can imply the multiplicity one property for Siegel cusp forms of degree 2, linking two important concepts in automorphic forms.

Contribution

It establishes a novel implication from a weak form of Bocherer's conjecture to the multiplicity one theorem for degree 2 Siegel cusp forms.

Findings

A weak form of Bocherer's conjecture implies multiplicity one.

The connection between conjecture and multiplicity one is established.

Provides new insights into automorphic form theory.

Abstract

We show that a weak form of the generalized Bocherer's conjecture implies multiplicity one for Siegel cusp forms of degree 2.