Abstract Average values over integral points on a three-dimensional sphere with an arbitrary smooth weight function are studied. For them, an expansion of the mean product of two L-series associated with the Hecke basis in spaces of holomorphic parabolic forms of integer even weight with respect to the congruence subgroup Γ 0 (4) is obtained.

中文翻译：

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三维球面上积分点的迹公式

摘要 研究了具有任意光滑权函数的三维球面上积分点的平均值。对于他们，获得了关于同余子群 Γ 0 (4) 的整数偶权全纯抛物线形式空间中与 Hecke 基相关的两个 L 级数的平均积的展开。