On the Periods of Ikeda-Yamana Lift for the Unitary Group I

TL;DR

This paper expresses the periods of certain lifted Hermitian modular forms on unitary groups in terms of special values of L-functions, extending previous results related to Ikeda's conjecture.

Contribution

It provides a new explicit formula for periods of Ikeda-Yamana lifts on unitary groups in terms of L-functions, generalizing Katsurada's earlier work.

Findings

Expressed the period of I_n(f) in terms of L-values.

Extended Katsurada's result on Ikeda's conjecture.

Connected Hermitian modular forms with automorphic L-functions.

Abstract

Let $F$ be a totally real field and $E$ be a quadratic CM extension field of $F$. Let $n$ be a positive integer. We denote by $\mathrm{I}_n$ the lift of the Hermitian modular form of weight $(w_{\lambda})_{\lambda}$ with level 1 to unramified automorphic forms defined on the unitary group constructed by Yamana. We then express the period $\langle{\mathrm{I}_n(f), \mathrm{I}_n(f)}\rangle$ of $\mathrm{I}_n(f)$ for Hecke eigenforms $f$ in terms of special values of some types of $L$-functions of $f$. This is an extension of Katsurada's result concerning Ikeda's conjecture.