, Volume 213, Issue 2, pp 433-470

Distribution of Lattice Points Visible from the Origin

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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 C 1 boundary. For each integer Q≥ 1, we consider the integer lattice points from which are visible from the origin and prove that the 1 st consecutive spacing distribution of the angles formed with the origin exists. This is a probability measure supported on an interval [m Ω,∞), with m Ω >0. Its repartition function is explicitly expressed as the convolution between the square of the distance from origin function and a certain kernel.

Received: 2 November 1999 / Accepted: 2 March 2000