Primitive lattice points in narrow boundary layers of convex planar domains.
Abstract
A primitive lattice point (in the plane) is a point with integer coordinates (u,v) which are relatively prime to each other. We consider a convex planar domain D which contains the origin as an inner point, whose boundary is sufficiently smooth and of finite nonzero curvature throughout. For a large real variable x let xD denote the domain D 'blown up' by the factor x. We ask for the number of primitive lattice points in the 'boundary layer' (x+h)D - xD, where h is another real variable but of smaller order of magnitude than x (e.g., h = xa, a<1). How small can h be compared to x such that for the quantity under consideration an asymptotic formula can be established? As an auxiliary result we need an asymptotic evaluation of the number of all lattice points in a certain suitable three-dimensional body.
keywords primitive lattice points convex planar domains exponential sums
Publikationen
Primitive lattice points in a thin strip along the boundary of a large convex planar domain.
Autoren: Krätzel, E., Nowak, W.G. Jahr: 2001
Journal articles
Project staff
Werner Georg Nowak
Em.O.Univ.Prof. Dr.phil. Werner Georg Nowak
werner_georg.nowak@boku.ac.at
Project Leader
01.06.1996 - 31.12.2000
BOKU partners
External partners
Cardiff Metropolitan University
Prof. Dr. Martin Huxley, School of Mathematics
partner
University of Wienna, Institute of Mathematics
Prof. Dr. Ekkehard Krätzel
coordinator