THE CORRELATIONS OF FAREY FRACTIONS

DOI10.1112/S0024610705006629zbMath1089.11037arXivmath/0404114MaRDI QIDQ5693014

Florin P. Boca, Alexandru Zaharescu

Publication date: 28 September 2005

Published in: Journal of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0404114

Mathematics Subject Classification ID

Well-distributed sequences and other variations (11K36) Farey sequences; the sequences (1^k, 2^k, dots) (11B57) Distribution modulo one (11J71)

Related Items (15)

A note on the pair correlation of Farey fractions ⋮ Pair correlation of roots of rational functions with rational generating functions and quadratic denominators ⋮ Pair correlation of hyperbolic lattice angles ⋮ The distribution of free path lengths in the periodic Lorentz gas and related lattice point problems ⋮ Pair correlations of logarithms of complex lattice points ⋮ \(k\)-moments of distances between centers of Ford circles ⋮ On the correlations of directions in the Euclidean plane ⋮ Pair correlation of rationals with prime denominators ⋮ Hutchinson-Zaharescu parabolas and Ford circles ⋮ Correlation of fractions with divisibility constraints ⋮ Pair correlation of torsion points on elliptic curves ⋮ Limiting distribution of eigenvalues in the large sieve matrix ⋮ On the pair correlation density for hyperbolic angles ⋮ On the statistics of pairs of logarithms of integers ⋮ Poincaré sections for the horocycle flow in covers of \(\mathrm {SL}(2,\mathbb {R})/\mathrm {SL}(2,\mathbb {Z})\) and applications to Farey fraction statistics

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