9700488 Stopple/Imamoglu This award funds research by the second named principal investigator on the following topics. First, she proposes to investigate a series of conjectural liftings from classical modular forms to Siegel modular forms. Second, she proposes to establish a Kronecker limit formula for the symplectic group of degree 4. This involves finding the Laurent series expansion of Siegel Eisenstein series about its pole. Such a result would have applications to arithmetic and geometry. Third, with J. Hoffstein, she proposes to develop a generalization of metaplectic forms. These new forms, as in the case of metaplectic forms, are expected to lead to striking results in the theory of L-functions. Last, jointly with L. Walling, she proposes to work on generalized Jacobi theta functions. These theta functions can also be used to make an appropriate Saito-Kurokawa conjecture since they provide a constructive example of such a lift. This research falls into the general mathematical field of Number Theory. Number Theory has its historical roots in the study of the whole numbers, addressing such questions as those dealing with the divisibility of one whole number by another. It is among the oldest branches of mathematics and was pursued for many centuries for purely aesthetic reasons. However, within the last half century it has become an indispensable tool in diverse applications in areas such as data transmission and processing, and communication systems.
