Mathematical Sciences: Analytic Number Theory on Groups

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Professor Goldfeld will work on several problems connected with automorphic forms. In particular, he will study special values of the derivative of L-functions and determine if a cohomology theory of special values of L-functions can be developed. Automorphic forms arose out of Non-Euclidean geometry in the middle of the nineteenth century. Both mathematicians and physicists have thus long realized that many objects of fundamental importance are non-Euclidean in their basic nature. This field is principally concerned with questions about the whole numbers, but in its use of geometry and analysis, it retains connection to its historical roots and thus to problems in areas as diverse as gauge theory in theoretical physics and coding theory in information theory.