On generalized Maass relations for the Miyawaki-Ikeda lift

TL;DR

This paper generalizes the Maass relation for Siegel-Eisenstein series of any degree and demonstrates its application in analyzing Miyawaki-Ikeda lifts, providing new proofs and L-function computations.

Contribution

It introduces a new generalized Maass relation for Siegel-Eisenstein series and applies it to Miyawaki-Ikeda lifts, offering novel proofs and insights.

Findings

Generalized Maass relation for arbitrary degree Siegel-Eisenstein series

Verification that Duke-Imamoglu-Ibukiyama-Ikeda lifts satisfy this relation

New computation of the standard L-function for Miyawaki-Ikeda lifts

Abstract

Some generalizations of the Maass relation for Siegel modular forms of higher degrees have been obtained by several authors. In the present article we first give a new generalization of the Maass relation for Siegel-Eisenstein series of arbitrary degrees. Furthermore, we show that the Duke-Imamoglu-Ibukiyama-Ikeda lifts satisfy this generalized Maass relation with some modifications. As an application of the generalized Maass relation in the present article we give a new proof of the Miyawaki-Ikeda lifts of two elliptic modular forms. Namely, we compute the standard L-function of the Miyawaki-Ikeda lifts of two elliptic modular forms by using the generalized Maass relation.