Algebraicity of special $L$-values attached to Siegel-Jacobi modular forms

TL;DR

This paper proves algebraicity results for special L-values linked to Siegel-Jacobi modular forms, extending the doubling method and introducing near holomorphy concepts.

Contribution

It generalizes the doubling method to the Jacobi group and introduces near holomorphy for Siegel-Jacobi forms, advancing the understanding of their L-values.

Findings

Algebraicity of certain special L-values established.

Extended doubling method to the Jacobi group.

Developed near holomorphy concept for Siegel-Jacobi forms.

Abstract

In this work we obtain algebraicity results on special $L$-values attached to Siegel-Jacobi modular forms. Our method relies on a generalization of the doubling method to the Jacobi group obtained in our previous work, and on introducing a notion of near holomorphy for Siegel-Jacobi modular forms. Some of our results involve also holomorphic projection, which we obtain by using Siegel-Jacobi Poincar\'e series of exponential type.