Abstract Let U / Q be a unitary group of Q -rank one so that the group of real points U ( R ) ≅ U ( n , 1 ) . The group U is only quasi-split over Q if and only if n = 1 , 2 . The cohomology of a congruence subgroup of U is closely related to the theory of automorphic forms. This relation is best captured in the so-called automorphic cohomology spaces H ⁎ ( U , C ) , a natural module under the action of the group U ( A f ) . This paper gives a structural account of the U ( A f ) -module structure of that part of the cohomology which is generated by residues or derivatives of Eisenstein series. In particular, we determine a set of arithmetic conditions, mainly given in terms of partial automorphic L-functions, subject to which residues of Eisenstein series may give rise to non-vanishing cohomology classes. The main task is, although the usual method due to Langlands-Shahidi is not applicable, to analyze the analytic behavior of suitable Eisenstein series and to determine the location of their possible poles.

中文翻译：

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秩一酉群的爱森斯坦级数和一些上同调应用

摘要 令U/Q 为Q-秩一的酉群，使得实点群U(R)≅U(n,1)。当且仅当 n = 1 , 2 时，组 U 才在 Q 上准分裂。U 的同余子群的上同调与自守形式理论密切相关。这种关系在所谓的自守上同调空间 H ⁎ (U, C) 中得到了最好的捕捉，这是群 U (A f ) 作用下的一个自然模块。本文给出了由爱森斯坦系列的残基或衍生物产生的那部分上同调的 U ( A f ) -模结构的结构说明。特别是，我们确定了一组算术条件，主要是根据部分自守 L 函数给出的，在此条件下，爱森斯坦级数的残差可能会产生非消失的上同调类。主要任务是，