Mathematical Sciences: Special Values of L-series Associated to Hecke Characters

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Special values of L-functions play an important role in modern number theory, lying between analysis and arithmetic as in, for example, the conjectures of Birch and Swinnerton-Dyer. This research project concerns special values of L-series associated to Hecke characters. Its chief goal is to establish a direct connection between previous results of the principal investigator and the theory of theta lifts and automorphic representations. A particularly interesting case is that of the symmetric square of an elliptic curve. 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.