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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
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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