-
Irreducible cuspidal representations with prescribed local behavior
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 133, Number 5, October 2011
- pp. 1231-1258
- 10.1353/ajm.2011.0035
- Article
- Additional Information
Let $G$ be a simple algebraic group defined over the global field $k$. In this paper, we use the simple
trace formula 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.