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

n 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