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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
Werner Georg Nowak
Affiliation:
Institut für Mathematik der Universität für Bodenkultur, Gregor Mendel-Straße 33, A-1180 Wien, Austria
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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
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 100 , Issue 3-4 , 1985 , pp. 295 - 299
Copyright
Copyright © Royal Society of Edinburgh 1985

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