Arithmetic of L-Values

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9401553 Stevens This award funds the research of Prof. Glenn Stevens into connections between Number Theory and Algebraic Geometry. In particular Prof. Stevens will study the arithmetic properties of modular symbols. He also hopes to make progress in the understanding of the exceptional zero conjecture of Mazur, Tate and Teitelbaum from higher rank and from higher weight. This is research in the field of number theory. Number theory is basically the study of whole numbers. The research done under this award studies properties of the whole numbers by encoding them into functions called modular forms. Number theory is among the oldest fields of mathematics, yet it has always played an important role in choosing directions for the rest of the subject. Within the last half century, the study of whole numbers has become doubly important as the theory has been used to develop new algorithms for computer science and to construct new error correcting codes for electronics.