On the spinor L-function of Miyawaki-Ikeda lifts

TL;DR

This paper investigates the spinor L-functions of Miyawaki-Ikeda lifts, showing they decompose into products of symmetric power L-functions derived from two original elliptic modular forms, under a non-vanishing assumption.

Contribution

It establishes a factorization of spinor L-functions for Miyawaki-Ikeda lifts into symmetric power L-functions, advancing understanding of their structure.

Findings

Spinor L-functions decompose into symmetric power L-functions.

Factorization holds under a non-vanishing assumption.

Provides insight into the L-function structure of Miyawaki-Ikeda lifts.

Abstract

We consider lifts from two elliptic modular forms to Siegel modular forms of odd degrees which are special cases of Miyawaki-Ikeda lifts. Assuming non-vanishing of these Miyawaki-Ikeda lifts, we show that the spinor L-functions of these Miyawaki-Ikeda lifts are products of some kind of symmetric power L-functions determined by original two elliptic modular forms.