# 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.

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