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Poisson spacings for lattice points on circles

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Speaker: 
Pär Kurlberg
Zugehörigkeit: 
KTH
Datum: 
Fre, 09/05/2025 - 10:30 - 10:55
Location: 
MPIM Lecture Hall

We will investigate the distribution of $Z^2$-lattice points lying on circles. Along a density one subsequence the angles of lattice points on circles are known to be uniformly distributed as the radius tends to infinity; in fact the angles are "very well distributed" in the sense of the discrepancy being lower than that of a random collection of
points. A refined question is how lattice points are spaced at the local scale, i.e., when rescaled so that the mean spacing is one. I will discuss joint work with Steve Lester in which we show that the local spacing statistics are Poissonian along a density one subsequence of admissible radii.

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