On the Periods of Ikeda-Yamana Lift for the Unitary Group I
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918517314420736 |
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| author | Higashitani, Jin |
| author_facet | Higashitani, Jin |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_18294 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Periods of Ikeda-Yamana Lift for the Unitary Group I Higashitani, Jin Number Theory 11F67 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. |
| title | On the Periods of Ikeda-Yamana Lift for the Unitary Group I |
| topic | Number Theory 11F67 |
| url | https://arxiv.org/abs/2605.18294 |