Mathematical Sciences: Theta Functions and Eisenstein Serieson the Metaplectic Group

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This award supports the research of Professor J. Hoffstein to work in automorphic functions. He intends to work on obtaining the symmetric cube L-series of a cusp form on GL(2) as a Rankin Selberg integral. He also intends to study non-unique Whittaker models of theta functions on the n-fold cover of GL(2). Modular 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.