This paper completes the construction of $p$ -adic $L$ -functions for unitary groups. More precisely, in Harris, Li and Skinner [‘ $p$ -adic $L$ -functions for unitary Shimura varieties. I. Construction of the Eisenstein measure’, Doc. Math.Extra Vol. (2006), 393–464 (electronic)], three of the authors proposed an approach to constructing such $p$ -adic $L$ -functions (Part I). Building on more recent results, including the first named author’s construction of Eisenstein measures and $p$ -adic differential operators [Eischen, ‘A $p$ -adic Eisenstein measure for unitary groups’, J. Reine Angew. Math.699 (2015), 111–142; ‘ $p$ -adic differential operators on automorphic forms on unitary groups’, Ann. Inst. Fourier (Grenoble)62(1) (2012), 177–243], Part II of the present paper provides the calculations of local $\unicode[STIX]{x1D701}$ -integrals occurring in the Euler product (including at $p$ ). Part III of the present paper develops the formalism needed to pair Eisenstein measures with Hida families in the setting of the doubling method.

中文翻译：

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-ADIC -单位群的函数

这篇论文完成了构建 $p$ -adic $L$ - 酉组的功能。更准确地说，在哈里斯、李和斯金纳 [' $p$ -adic $L$ - 单一志村品种的功能。I. 爱森斯坦测度的构造'，博士。数学。额外卷。(2006), 393–464 (electronic)]，三位作者提出了一种构建这种 $p$ -adic $L$ -函数（第一部分）。基于最近的结果，包括第一作者构建的爱森斯坦度量和 $p$ -adic 微分算子 [Eischen, 'A $p$ - 酉群的进阶爱森斯坦测度，J. Reine Angew。数学。699(2015), 111–142; ' $p$ - 酉群上自守形式的进数微分算子，安。研究所。傅立叶（格勒诺布尔）62(1) (2012), 177-243], 本文的第二部分提供了局部的计算 $\unicode[STIX]{x1D701}$ -欧拉积中出现的积分（包括在 $p$ ）。本文的第三部分发展了在加倍方法的设置中将爱森斯坦测量与飞騨族配对所需的形式主义。