Algebraicity of special $L$-values attached to Siegel-Jacobi modular 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 Poincaré series of exponential type.

This article forms a significant extension of the last section of our previous paper arXiv:1706.07287. 41 pages