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arXiv · 0708.0114

Shintani Cocycles on $\GL_{n}$

Richard Hill
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Abstract

The aim of this paper is to define an n-1-cocycle $σ$ on $\GL_{n}(\Q)$ with values in a certain space $\hD$ of distributions on $\A_f^{n}\setminus\{0\}$. Here $\A_f$ denotes the ring of finite adèles of $\Q$, and the distributions take values in the Laurent series $\C((z_{1},...,z_{n}))$. This cocycle can be used to evaluate special values of Artin L-functions on number fields at negative integers. The construction generalizes that of Solomon in the case n=2.

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Richard Hill. 2007-08-01. Shintani Cocycles on $\GL_{n}$. https://doi.org/10.1112/blms%2Fbdm099

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