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Speaker:
Pär Kurlberg
Zugehörigkeit:
KTH
Datum:
Fre, 09/05/2025 - 10:30 - 10:55
Location:
MPIM Lecture Hall
Parent event:
Conference on "Asymptotic Counting and L-Functions" 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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