Irreducible cuspidal representations with prescribed local behavior

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.