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arXiv · 2605.18294

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

Jin Higashitani
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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 $(\kappa_v)_{v|\infty}$ 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.

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Jin Higashitani. 2026-05-18. On the Periods of Ikeda-Yamana Lift for the Unitary Group I. https://arxiv.org/abs/2605.18294

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