Differential Operators for Siegel-Jacobi forms

2013/01/07 by Jiong Yang, Yang, Jiong, Linsheng Yin +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical Analysis and Transform Methods #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1301.1156

openalex publication_date 2013/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any positive integers n and m, ℍ_n,m:=ℍ_n×ℂ^(m,n) is called the Siegel-Jacobi space, with the Jacobi group acting on it. The Jacobi forms are defined on this space. In this article we compute the Chern connection of the Siegel-Jacobi space and use it to obtain derivations of Jacobi forms. Using these results, we constructed a series of invariant differential operators for Siegel-Jacobi forms. Also two kinds of Maass-Shimura type differential operators for ℍ_n,m are obtained.

Related

• A note on invariant differential operators on Siegel-Jacobi space
• Invariant Differential Operators on Siegel-Jacobi Space
• Rankin-Cohen Operators for Jacobi and Siegel Forms
• Differential operators on Hermitian modular forms on U(n, n)
• Derivations of Siegel Modular Forms from Connections