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

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.

MSC:

22E50 Representations of Lie and linear algebraic groups over local fields

Keywords:

\(L\)-functions
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