Volodymyr Pavlenkov

collaborators

4 papers

math.NT2026

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…

math.NT2026

Positive Logarithmic Hausdorff Measures of Exceptional Sets for the $p$ -adic and $t$ -adic Littlewood Conjectures

Dzmitry Badziahin, Volodymyr Pavlenkov, Evgeniy Zorin

We prove that if the exceptional set $E_{p}$ for the $p$ -adic Littlewood conjecture is non-empty, then its logarithmic Hausdorff dimension is at least one. More precisely, whenever $…

math.NT2026

Rational Points and Brownian Motion

Faustin Adiceam, Volodymyr Pavlenkov, Evgeniy Zorin

Given a real-valued function $f$ , let $N_{f} (δ, Q)$ be the number of rational points with denominators at most $Q \geq 1$ in the $(δ / Q)$ -tubular neighbourhood of the graph of…

math.NT2024

Inhomogeneous Diophantine Approximation on $M_{0}$ -sets

Volodymyr Pavlenkov, Evgeniy Zorin

We prove new quantitative Schmidt-type theorem for Diophantine approximations with restraint denominators on fractals (more precisely, on $M_{0}$ -sets). Our theorems introduce a shar…

Rational Points near Monofractal Curves and the Strong Oscillation Principle

Positive Logarithmic Hausdorff Measures of Exceptional Sets for the p-adic and t-adic Littlewood Conjectures

Rational Points and Brownian Motion

Inhomogeneous Diophantine Approximation on M0​-sets

Positive Logarithmic Hausdorff Measures of Exceptional Sets for the $p$ -adic and $t$ -adic Littlewood Conjectures

Inhomogeneous Diophantine Approximation on $M_{0}$ -sets