FINITE FIELDS AND APPLICATIONS Characters and character sums (9 lectures)
نویسنده
چکیده
Exponential sums and character sums have many applications in number theory and combinatorial number theory. Many famous and interesting problems have been studied by means of exponential sums techniques: Goldbach ternary conjecture (Vinogradov), Waring Problem (Hardy, Littlewood, Vaughan, Vinogradov, Wooley), Distribution of prime numbers (Ford, Hardy, Korobov, Linnik,...) as well as many other interesting questions. The applications of these techniques are so wide, that they represent a very active research area nowadays. In this short introductory course we will discuss some basic theory of characters, focusing on the finite field case, and show some classic examples of character sums as well as some applications.
منابع مشابه
Exponential sums over finite fields, II: introduction to cohomological methods
Contents Chapter 1. Introduction 1 1. Why is the one-variable theory not sufficient? 1 2. Outline of the rest of the book 1 Chapter 2. Background material: algebraic geometry 3 1. Affine algebraic varieties 3 2. First examples 7 3. Computing with algebraic varieties 7 Chapter 3. Summands for algebraic exponential sums 8 1. From Dirichlet characters to Galois characters 8 2. From Galois groups t...
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