Volodymyr Pavlenkov

collaborators

3 papers

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…

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