11. His main contribution and impact was in the area of automorphic forms and L-functions. 12. This fact makes the ad�le groups very effective as tools in the theory of automorphic forms . 13. Equivalently, an automorphic form is a function whose divisor is invariant under the action of G. 14. The " factor of automorphy " for the automorphic form f is the function j. 15. An " automorphic function " is an automorphic form for which j is the identity. 16. In another direction the classical topic of modular forms has blossomed into the modern theory of automorphic forms . 17. Automorphic forms are a generalization of the idea of periodic functions in Euclidean space to general topological groups.18. For example, representation theory is used in the modern approach to gain new results about automorphic forms . 19. Originally defined for the modular group, Eisenstein series can be generalized in the theory of automorphic forms . 20. Casselman specializes in representation theory, automorphic forms , geometric combinatorics, and the structure of algebraic groups.
