Mathematical Sciences: Zeta Functions and Automorphic Forms

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The investigations of this proposal will be made on number- theoretical problems dealing with zeta functions and automorphic forms. The Fourier coefficients of automorphic forms, Eisenstein series, and the special values of certain zeta functions are the main objects of study. This is research in the field of number theory. Number theory starts with the whole numbers and questions such as the divisibility of one whole number by another. It is among the oldest fields of mathematics and it was originally pursued for purely aesthetic reasons. However, within the last half century, it has become an essential tool in developing new algorithms for computer science and new error correcting codes for electronics.