\(L\)-functions for Jacobi forms on \(\text{H} \times \mathbb{C}\)
The purpose of this article is the investigation of Jacobi forms of degree \(n\) and scalar index \(t\) and of the analytic properties of \(L\)-functions associated to them. The method used is a modification of the pullback method of Böcherer and Garrett from the case of Siegel modular forms. For square free index \(t\) the author obtains a Rankin-Selberg integral representation of the \(L\)-function using a rationality theorem for the Hecke algebra. Similar results have been obtained by \textit{A. Murase} and, respectively, by \textit{T. Sugano} [Math. Ann. 290, 247-276 (1991; Zbl 0721.11022), Comment. Math. Univ. St. Pauli 44, 1-58 (1995; Zbl 0840.11021)].
scientific article; zbMATH DE number 1003988