A Note on Maass-Jacobi Forms II

Abstract

This article is a continuation of the paper [21]. In this paper we deal with Maass-Jacobi forms on the Siegel-Jacobi space H × C m , where H denotes the Poincaré upper half plane and m is any positive integer.

A note on the Schottky problem

“…Describe J g,h in terms of Jacobi forms. We refer to [17,42,156,157,159,160,161,163,164,165,166,167,175,178,189] for more details about Jacobi forms. Problem 7.2.…”

Geometry and Arithmetic on the Siegel–Jacobi Space

“…In the sense of Definition 11.2, Pitale [50] studied Maass-Jacobi forms on the Siegel-Jacobi space H 1,1 . We refer to [74,75] for more details on Maass-Jacobi forms.…”

Adjoint orbits of the Jacobi group

“…Therefore the Jacobi group G J plays an important role in number theory (e.g. theory of Jacobi forms) [4,13,14,15,16,17,18,27,29,32,33], algebraic geometry [20,22,29,31], complex geometry [23,24,25,26,29], representation theory [2,28,30] and mathematical physics [1,8].…”