L-functions of Several Complex Variables and Automorphic Forms

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The research of Imamoglu focuses on the analytic theory of L-series of several complex variables. The PI and her collaborators have recently defined Rankin-Selberg Dirichlet series of several complex variables attached to Siegel cusp forms. She proposes to exploit the analytic properties of these series to establish non-vanishing results for special values of Rankin-Selberg convolutions of Fourier_Jacobi coefficients of Siegel forms and to improve bounds for their classical Fourier coefficients. She also proposes to investigate a possible generalization of the classical Dedekind zeta function of a number field to a zeta function of several complex variables.The investigations of this proposal belong to number theory, which is a branch of mathematics that deals with problems involving whole numbers. Mathematicians have discovered that many of the important properties of whole numbers can be encoded into certain objects called "L-functions". These L-functions have their origin in the study of calculus but our understanding of their fundamental properties are far from complete. The PI and her collaborators proposes to investigate the analytic properties of these functions to fill in some of the gaps in our knowledge.