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

谢赫 该奖项资助罗伯特·斯切赫教授在解析数论方面的研究。 Schzech教授计划在整数上的n维一般线性群的Eilenberg-MacLane上同调中明确地构造某些Eisenstein上循环。 这些构造的最终目的是研究数论中特殊L-函数的特殊值。 这是解析数论领域的研究。 数论是研究整数的性质。 在解析数论中，整数的性质是通过将数字编码到微积分的函数中来检验的。 数论是数学中最古老的领域之一，但它在选择其他学科的方向方面一直发挥着重要作用。 在过去的半个世纪，研究整数已成为双重重要的理论已被用来开发新的算法，计算机科学和构造新的纠错码的电子。***

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. ***