On ratios of Petersson norms for Yoshida lifts

TL;DR

This paper proves an algebraicity property for a ratio of Petersson norms related to Siegel cusp forms of degree 2, connecting automorphic representations and endoscopic lifts.

Contribution

It establishes algebraicity of Petersson norm ratios for Siegel cusp forms linked to weak endoscopic lifts, expanding understanding of their automorphic properties.

Findings

Proves algebraicity of Petersson norm ratios for specific Siegel cusp forms

Details the correspondence between scalar Siegel cusp forms and automorphic representations

Explores features of endoscopic lift automorphic representations

Abstract

We prove an algebraicity property for a certain ratio of Petersson norms associated to a Siegel cusp form of degree 2 (and arbitrary level) whose adelization generates a weak endoscopic lift. As a preparation for this, we explicate various features of the correspondence between scalar valued Siegel cusp forms of degree n and automorphic representations on GSp_{2n}.