Mathematical Sciences: Eisenstein Cocycles for Arithmetic Groups and Values of L-functions

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Sczech This award funds the research of Professor Robert Sczech in analytic number theory. Prof. Sczech plans to explicitly construct certain Eisenstein cocycles in the Eilenberg-MacLane cohomology of the general linear group of dimension n over the integers. The ultimate aim of these constructions is to study the special values of particular L-functions in number theory. This is research in the field of analytic number theory. Number theory is the study of properties of the whole numbers. In analytic number theory properties of whole numbers are examined by encoding numbers into the functions of calculus. 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. ***