Shimura varieties and twisted orbital integrals
Langlands' work on the Shimura varieties attached to quaternion algebras over totally real number fields led him to outline an attack on the problem of expressing the zeta function of a general Shimura variety in terms of automorphic L-functions. He divided his approach into parts, one of them being a combinatorial problem which arises during the comparison of the Selberg trace formula with the number of points on the Shimura variety over a finite field. The author of this paper shows that Langlands' combinatorial problem can be reduced to a standard problem in local harmonic analysis: that of establishing the spherical function identities needed for base change.
scientific article; zbMATH DE number 3845737
scientific article