中法班学术报告003【郗　平】

摘要：Applications of Fourier analysis to number theory create exponential sums, which are basically of analytic or algebraic types. Estimates for such exponential sums turn out to be very crucial in many applications. In this talk, we aim to give a survey on the study of algebraic exponential sums from different aspects, including complete sums and incomplete sums, one variable cases and high dimensional generalizations, analytic methods and geometric approaches, arithmetic properties and analytic behaviours, individual sums and on average. With some typical examples on hand, we would like to show how algebraic exponential sums are applied in analytic number theory, and also describe how the latter one is used to characterize the former ones.