ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

3. Number Theory and Arithmetic Algebraic Geometry

1991 MS Classification: Puchta, Jan-Christoph, Universität Freiburg Estimating Dirichlet L-serieses close to the line 1 + it Using higher derivatives of Dirichlet L-serieses known estimates for |L(s, χ)| can be improved. As application I can show that for the relative class number h^{+} of the p-th cyclotomic field the estimate log h^{+} = \frac{p}{4} log p − \frac{p}{2} log 2π +log(1−β)+O(log^{2}p), where β is a Siegel zero, if p ≡ 3 (mod 4), otherwise this term does not occur at all. As another application the width of zerofree regions can be improved slightly.