We study weighted versions of Dirichlet's theorem on the probability that two integers, taken at random, are relatively prime. This leads to a uniform approach in the study of several counting problems in discrete and computational geometry relating to incidences between points and lines.

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Persistent URL dx.doi.org/10.1016/0925-7721(94)00013-1
Journal Computational Geometry
Kranakis, E, & Pocchiola, M. (Michel). (1994). Counting problems relating to a theorem of Dirichlet. Computational Geometry, 4(6), 309–325. doi:10.1016/0925-7721(94)00013-1