4 papers · 1 filter
Rational Points near Monofractal Curves and the Strong Oscillation Principle
Faustin Adiceam, Volodymyr Pavlenkov, Evgeniy Zorin
In their previous work devoted to the distribution of rational points near Brownian motion, the authors conjectured the existence of an \emph{oscillation principle} governing the a…
Kronecker sequences beyond the torus: nearest-neighbour distances and best returns
Evgeniy Zorin
The classical three-gap theorem says that a finite Kronecker sequence on the circle has at most three gap lengths. We extend this phenomenon to nearest-neighbour distances on quoti…
Positive Logarithmic Hausdorff Measures of Exceptional Sets for the -adic and -adic Littlewood Conjectures
Dzmitry Badziahin, Volodymyr Pavlenkov, Evgeniy Zorin
We prove that if the exceptional set for the -adic Littlewood conjecture is non-empty, then its logarithmic Hausdorff dimension is at least one. More precisely, whenever $…
Rational Points and Brownian Motion
Faustin Adiceam, Volodymyr Pavlenkov, Evgeniy Zorin
Given a real-valued function , let be the number of rational points with denominators at most in the -tubular neighbourhood of the graph of…