Mathematical Sciences: The Weil-Siegel Formula and Its Applications

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This project consists of several problems in the theory of automorphic forms and L-functions. The first problem concerns extending the Weil-Siegel formula and applying this extension. The second concerns the application of the theory of seesaw dual pairs to study arithmetic properties of certain automorphic forms. Research will also be done on the structure of Clifford algebras, as well as, the cohomology classes associated to certain geodesic cycles. This research is in the general area of number theory. It is concerned with various aspects of representation theory in its application to automorphic forms and number theory. The principal investigator has in the past evolved some penetrating results in the area of automorphic functions on bounded domains. New and exciting developments in the areas considered in this project are anticipated.