Distribution of Lattice Points Visible from the Origin
- Cite this article as:
- Boca, F., Cobeli, C. & Zaharescu, A. Commun. Math. Phys. (2000) 213: 433. doi:10.1007/s002200000250
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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 \(\) 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.