# Journal of the Ramanujan Mathematical Society

Volume 29, Issue 4, December 2014  pp. 379–402.

Pullbacks of Klingen-Eisenstein series attached to Jacobi cusp forms

Authors:  Shin-ichiro Mizumoto
Author institution:Department of Mathematics, Tokyo Institute of Technology, Oo-okayama, Meguro-ku, Tokyo, 152-8551, Japan

Summary:  Let F be a Siegel cusp form of degree n ≥ 2 and φ be a Jacobi cusp form of degree r (< n) and index T, where T is a kernel form of size n - r. Suppose F and φ are eigenfunctions of the Hecke operators. Let [φ] rn ((Z, w), s) be the Klingen-Eisenstein series of degree $n$ attached to φ. We show that the Petersson inner product ([φ] rn ((Z, 0), s), F(Z)) is essentially equal to the quotient of the standard L-function of F and that of φ. Our result is a generalization of the result of Heim [9] which treated the case n = 2, r = 1.