Communications in Mathematical Physics

, Volume 213, Issue 2, pp 433–470

Distribution of Lattice Points Visible from the Origin

  • Florin P. Boca
  • Cristian Cobeli
  • Alexandru Zaharescu

DOI: 10.1007/s002200000250

Cite this article as:
Boca, F., Cobeli, C. & Zaharescu, A. Commun. Math. Phys. (2000) 213: 433. doi:10.1007/s002200000250

Abstract:

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 \(\) 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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Florin P. Boca
    • 1
  • Cristian Cobeli
    • 2
  • Alexandru Zaharescu
    • 2
  1. 1.School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF2 4YH, UKGB
  2. 2.Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Bucharest 70700, RomaniaRO
  3. 3.Institute for Advanced Study, School of Mathematics, Olden Lane, Princeton, NJ 08540, USAUS

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