Algebraicity of critical values of adjoint $L$-functions for ${\rm GSp}_4$

TL;DR

This paper proves an algebraicity result for critical values of adjoint L-functions associated with GSp_4 over totally real fields, relating them to Petersson norms of cuspidal newforms, extending previous work.

Contribution

It generalizes prior algebraicity results for GSp_4 L-functions to totally real fields, connecting critical values with Petersson norms.

Findings

Established algebraicity of critical L-values for GSp_4 over totally real fields.

Extended previous results to a broader class of number fields.

Linked L-values to Petersson norms of automorphic forms.

Abstract

We prove an algebraicity result for certain critical value of adjoint $L$-functions for ${\rm GSp}_4$ over a totally real number field in terms of the Petersson norm of normalized generic cuspidal newforms on ${\rm GSp}_4$. This is a generalization of our previous result arXiv:1902.06429.