Irreducible cuspidal representations with prescribed local behavior. (English) Zbl 1228.22017

Gross, Benedict H.

Am. J. Math. 133, No. 5, 1231-1258 (2011).

Let \(G\) be a simple algebraic group over a global field \(k\). A simple trace formula is used to determine the sum of the multiplicities of the irreducible representations in the cuspidal spectrum of \(G\), with specified local behavior at a finite set of places of \(k\) and unramified elsewhere. This sum is expressed as the product of the values of modified Artin \(L\)-functions at negative integers.

Reviewer: L. N. Vaserstein (University Park)

MSC:

22E50

Representations of Lie and linear algebraic groups over local fields

Keywords:

\(L\)-functions