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