Exponential Sums as Algebraic Integers

报告题目:Exponential Sums as Algebraic Integers

报 告 人:Professor Daqing Wan(University of California, Irvine)



报告摘要:For a prime number p and an integral polynomial f(x), the associated exponential sum S_p(f) over the finite field of p elements is an algebraic integer in the p-th cyclotomic field. The exponential sum is a fundamental classical topic of research in number theory. In this talk, we discuss the basic problem of determining the degree of S_p(f) as an algebraic integer. This turns out to be a very interesting and yet wide open problem, dating back to Gauss (1804) who settled the case when f(x) = x^d is a monomial.

专家简介:Daqing Wan,美国加州大学欧文分校教授,教育部海外杰出青年,曾入选中科院百人计划,获得国际华人数学家晨兴(Morningside)数学银奖。