Mathematical Sciences: Zeta Functions and Automorphic Forms

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This award supports an investigation on number-theoretical problems on zeta functions and automorphic forms. The Euler products associated to automorphic forms, Eisenstein series, and the special values of certain zeta functions are the main objects of study. The theory of such Euler products (or zeta functions) is one of the central themes of modern number theory, and Eisenstein series are analytic functions inseparably connected to them. The investigation of special values of zeta functions is relatively new, but has become the subject of increasing interest. 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.