Distribution of lattice points visible from the origin

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Let Ω be a region in the plane which contains the origin, is star-shaped with respect to the origin and has a piecewise C1 boundary. For each integer Q ≥ 1, we consider the integer lattice points from ΩQ = {(Qx, Qy); (x, y) ∈ Ω} which are visible from the origin and prove that the 1st consecutive spacing distribution of the angles formed with the origin exists. This is a probability measure supported on an interval [mΩ, ∞), with mΩ > 0. Its repartition function is explicitly expressed as the convolution between the square of the distance from origin function and a certain kernel.

Original languageEnglish (US)
Pages (from-to)433-470
Number of pages38
JournalCommunications in Mathematical Physics
Issue number2
StatePublished - Sep 2000
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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