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On the average order of the lattice rest of a convex planar domain

Published online by Cambridge University Press:  24 October 2008

Werner Georg Nowak
Werner Georg Nowak
Affiliation:
Institut für Mathematik der Universität für Bodenkultur, A-1180 Vienna, Austria
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Extract

Let denote a compact convex subset of the Euclidean plane containing the origin as an inner point and assume that the boundary ∂ of is a C∞-image of the 1-torus with finite nonvanishing curvature throughout. As a generalization of the classical circle problem in analytic number theory we consider, for a large parameter t, the number A(t) of lattice points (of the standard lattice ℤ2) in the ‘blown up’ domain and define the ‘lattice rest’ by (where is the area of ).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 98 , Issue 1 , July 1985 , pp. 1 - 4
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

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