THE DISTRIBUTION OF LATTICE POINTS IN ELLIPTIC ANNULI

Author: Wigman, Igor

Source: Quarterly Journal of Mathematics, Volume 57, Number 3, 15 September 2006 , pp. 395-423(29)

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Abstract:

We study the distribution of the number of lattice points lying in thin elliptical annuli. It has been conjectured by Bleher and Lebowitz that if the width of the annuli tends to zero and their area tends to infinity, then the distribution of this number, normalized to have zero mean and unit variance, is Gaussian. This has been proved by Hughes and Rudnick for circular annuli whose width shrinks to zero sufficiently slowly. We prove this conjecture for ellipses whose aspect ratio is transcendental and strongly Diophantine, also assuming the width shrinks slowly to zero.

Document Type: Research article

DOI: http://dx.doi.org/10.1093/qmath/hai017

Publication date: 2006-09-15

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The Quarterly Journal of Mathematics publishes original contributions to pure mathematics. Areas such as algebra, differential geometry, and global analysis receive particular emphasis. However the journal avoids specialization.