发表机构
Kyoto University（京都大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文确定了CM扩张上Hermitian Klingen-Eisenstein级数的本原Fourier系数，通过拉回公式将其表示为Siegel Eisenstein级数系数与Petersson内积的乘积，并在假设下证明了$p$-整性。
AI 中文摘要
设$E/F$为CM扩张，且$1\le r<n$。我们确定了在$\nmathrm{U}_{n,n}$上由$\nmathrm{U}_{r,r}$的尖点形式诱导的Hermitian Klingen-Eisenstein级数在主同余水平下的本原Fourier系数。利用Hermitian Eisenstein级数的拉回公式，我们将Klingen-Eisenstein级数的归一化本原Fourier系数表示为Siegel Eisenstein级数的相应本原Fourier系数乘以一个显式构造的全纯自守形式的Petersson内积。该Petersson内积中的自守形式是Hermitian theta级数与次数$r$的Siegel Eisenstein级数乘积的有限和。在某些假设下，我们还证明了这些归一化本原Fourier系数的$p$-整性。
英文摘要
Let $E/F$ be a CM extension and let $1\le r<n$. We determine primitive Fourier coefficients of Hermitian Klingen-Eisenstein series on $\mathrm{U}_{n,n}$ induced from cusp forms on $\mathrm{U}_{r,r}$, at principal congruence level. Using the pullback formula for Hermitian Eisenstein series, we express a normalized primitive Fourier coefficient of a Klingen-Eisenstein series as the corresponding primitive Fourier coefficient of a Siegel Eisenstein series multiplied by a Petersson inner product with an explicitly constructed holomorphic automorphic form. The automorphic form in the Petersson inner product is a finite sum of products of Hermitian theta series and Siegel Eisenstein series of degree $r$. Under some hypotheses, we also prove the $p$-integrality of these normalized primitive Fourier coefficients.
Comments33 pages
