Shintani Cocycles on $\GL_{n}$

Abstract

The aim of this paper is to define an n-1-cocycle $\sigma$ 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.

14 pages. To appear in LMS Bulletin

Cited by in corpus (5)

• Topological polylogarithms and $p$-adic interpolation of $L$-values of totally real fields
• Canonical Equivariant Cohomology Classes Generating Zeta Values of Totally Real Fields
• $p$-adic Polylogarithms and $p$-adic Hecke $L$-functions for Totally Real Fields
• Shintani-Barnes cocycles and values of the zeta functions of algebraic number fields
• A proof of the refined class number formula of Gross