On the Correlations of Directions in the Euclidean Plane


Let R (ν) (x,y),Q denote the repartition of the ν-point correlation measure of the finite set of directions P(x,y)P , where P(x,y) is the fixed point (x, y) ∈ [0, 1) 2 and P is an integer lattice point in the square [−Q,Q]. We show that the average of the pair correlation repartition R (2) (x,y),Q over (x, y) in a fixed disc D0 converges as Q → ∞. More… (More)


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