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

Abstract

Let $F$ be a totally real field and $E$ be a quadratic CM extension field of $F$. Let $n$ be an odd positive integer. Yamana constructed a lift from Hermitian modular forms to automorphic forms on the unitary group. We denote by $\mathrm{I}_n(f)$ the form obtained by applying this lift to the Hermitian modular form $f$ of weight $(κ_v)_{v|\infty}$ and level 1. We then express the period $\perd{\mathrm{I}_n(f), \mathrm{I}_n(f)}$ of $\mathrm{I}_n(f)$ for Hecke eigenforms $f$ in terms of special values of certain $L$-functions attached to $f$. This is an extension of Katsurada's result concerning Ikeda's conjecture.