Spherical varieties and integral representations of L-functions
Spherical varieties and integral representations of L-functions
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L 函数的球面簇和积分表示
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发表时间：
2009
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通讯作者：
Y. Sakellaridis
中科院分区：
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作者：
Y. Sakellaridis
给出了L函数(周期积分、Rankin-Selberg积分)的积分表示方法的概念和统一的解释。这导致：(I)根据球面变元的某些嵌入的分类(只要后者可用)对这种积分进行分类的方法，(Ii)将意味着该方法的广泛推广的猜想，以及(Iii)对相对迹公式中的“权因子”现象的解释。我们还证明了独立感兴趣的结果，例如p-ady域上分裂群的球面变种的广义Cartan分解(遵循Gaitsgory和Nadler的论点)。
We present a conceptual and uniform interpretation of the methods of integral representations of L-functions (period integrals, Rankin-Selberg integrals). This leads to: (i) a way to classify such integrals, based on the classification of certain embeddings of spherical varieties (whenever the latter is available), (ii) a conjecture which would imply a vast generalization of the method, and (iii) an explanation of the phenomenon of “weight factors” in a relative trace formula. We also prove results of independent interest, such as the generalized Cartan decomposition for spherical varieties of split groups over p-adic fields (following an argument of Gaitsgory and Nadler).