Equidistribution of Farey sequences on horospheres in covers of and applications

DOI10.1017/etds.2019.71zbMath1455.37003arXiv1712.03258OpenAlexW2979719097WikidataQ114119490 ScholiaQ114119490MaRDI QIDQ5135918

Byron Heersink

Publication date: 24 November 2020

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.03258

zbMATH Keywords

Diophantine approximationequidistributionhorosphereFrobenius numbersFarey sequences

Mathematics Subject Classification ID

Farey sequences; the sequences (1^k, 2^k, dots) (11B57) Diophantine approximation in probabilistic number theory (11K60) The Frobenius problem (11D07) Homogeneous flows (37A17) Relations between ergodic theory and number theory (37A44)

Cites Work

• 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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• The asymptotic distribution of Frobenius numbers
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• A Poincaré Section for the Horocycle Flow on the Space of Lattices
• Distribution of approximants and geodesic flows
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• Effective Equidistribution of Rational Points on Expanding Horospheres
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• Equidistribution of primitive rational points on expanding horospheres
• On two problems of Erdös Szüsz and Turan concerning diophantine approximations
• Sous-groupes d'indice fini dans $SL\left( {n,Z} \right)$

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