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The Quarterly Journal of Mathematics Advance Access published online on December 16, 2005
The Quarterly Journal of Mathematics, doi:10.1093/qmath/hai017
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© The author 2005. Published by Oxford University Press. All rights reserved
Received February 2, 2005

Article

The distribution of lattice points in elliptic annuli

Igor Wigman 1 *

1 School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel

* To whom correspondence should be addressed.
Igor Wigman, E-mail: igorv{at}post.tau.ac.il


  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.


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