Mathematical Sciences: L-Functions of Number Fields and Automorphic Forms

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This project involves studies on two topics: 1) multiplicity of discriminants, class numbers and Artin L-functions, and 2) distribution of Hecke eigenvalues. In the first category, the main objective is to establish estimates for class group character sums which are relatively short with respect to the discriminant. On the second topic, the aim is to investigate the orthogonality and equidistribution of eigenvalues of Hecke operators. This research falls into the general area 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.