Dmitry Badziahin

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math.NT2026

Simultaneous Diophantine approximation on the three-dimensional Veronese curve: the complete Hausdorff dimension story

Dmitry Badziahin, Nikita Shulga

We determine the Hausdorff dimension of the intersection of the set $W_{3} (λ)$ of simultaneously $λ$ -well approximable points with the Veronese curve $\mathcal V_3 \subset \…

math.NT2025

Distance between cubics and rationals

Dmitry Badziahin

We investigate the following problem: what is the smallest possible distance between a cubic irrational $ξ$ and a rational number $p / q$ in terms of the height $H (ξ)$ and $q$ ? More…

math.NT2025

Generating random factorisations of polynomial values

Dmitry Badziahin

We construct algorithms that efficiently generate random factorisations of values $P (n)$ as products of two integers, where $P \in Z [x]$ is a given quadratic or cubic monic…

math.NT2025

Simultaneous Diophantine approximation on the three dimensional Veronese curve

Dmitry Badziahin

We compute the Hausdorff dimension of the set of simultaneously $λ$ -well approximable points on the Veronese curve in $\RR^3$ for $1/3 \leq λ \leq 3/5$ . This range for $λ$ was predicte…

math.NT2025

Estimating lower limit in the $p$ -adic Littlewood conjecture

Dmitry Badziahin

We verify that $lim inf_{q \to \infty} q \cdot ∣ q ∣_{p} \cdot ∣∣ q x ∣∣ < ε$ for all real $x$ , small primes $p$ and relatively small $ε$ . This result supports the famous $p$ -adic Littlewood co…

Simultaneous Diophantine approximation on the three-dimensional Veronese curve: the complete Hausdorff dimension story

Distance between cubics and rationals

Generating random factorisations of polynomial values

Simultaneous Diophantine approximation on the three dimensional Veronese curve

Estimating lower limit in the p-adic Littlewood conjecture

Estimating lower limit in the $p$ -adic Littlewood conjecture