ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

3. Number Theory and Arithmetic Algebraic Geometry

1991 MS Classification: 11T Winterhof, Arne, TU Braunschweig On Incomplete Character Sums Using a special ordering {x_{0}, …, x_{q−1}} of the elements of an arbitrary finite field F_{q} the classical Polya-Vinogradov bound is generalized to |∑_{ν=0}^{k−1} χ(a + x_{ν})| < q^{1/2}(1 + log q); a ∈ F_{q}, where χ denotes a non-trivial multiplicative character. Furthermore, it is investigated how far the improvements of D. A. Burgess for prime fields F_{p} can be extended to arbitrary finite fields. References: 1. A. Winterhof, On the distribution of powers in finite fields, Finite Fields and Appl. , to appear. 2. A. Winterhof, “On incomplete character sums”, Bericht 98/01, Institute für Mathematik, TU Braunschweig.