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An Ω-estimate for the lattice rest of a convex planar domain

Published online by Cambridge University Press:  14 November 2011

Werner Georg Nowak
Affiliation:
Institut für Mathematik der Universität für Bodenkultur, Gregor Mendel-Straße 33, A-1180 Wien, Austria

Synopsis

Let D be a compact convex planar domain containing the origin, the boundary of which is of class C∞ and has finite non-vanishing curvature throughout. For the number A(i) of lattice points in the “blown up” domain √tD, the estimate

is established. This is a generalization of Hardy's classical result for the circle problem. The proof is based on asymptotic formulae for certain exponential integrals due to E. Hlawka.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1985

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