D. Badziahin

activity

20062026

most citedOn multiplicatively badly approximable numbers

18 citations · 49 across the 19 of their papers we have counts for

collaborators

Showing 2010 · math.NTShow all

4 papers · 2 filters

math.NT2010

Inhomogeneous theory of dual Diophantine approximation on manifolds

Dzmitry Badziahin, Victor Beresnevich, Sanju Velani

The inhomogeneous Groshev type theory for dual Diophantine approximation on manifolds is developed. In particular, the notion of nice manifolds is introduced and the divergence par…

math.NT2010

Multiplicatively badly approximable numbers and generalised Cantor sets

Dzmitry Badziahin, Sanju Velani

Let p be a prime number. The p-adic case of the Mixed Littlewood Conjecture states that liminf_{q \to \infty} q . |q|_p . ||q x|| = 0 for all real numbers x. We show that with the…

math.NT2010★ 4 cited

The mixed Schmidt conjecture in the theory of Diophantine approximation

Dzmitry Badziahin, Jason Levesley, Sanju Velani

Let $D = (d_{n})_{n = 1}^{\infty}$ be a bounded sequence of integers with $d_{n} \geq 2$ and let $(i, j)$ be a pair of strictly positive numbers with $i + j = 1$ . We prove that the set o…

math.NT2010★ 6 cited

On a problem in simultaneous Diophantine approximation: Schmidt's conjecture

Dzmitry Badziahin, Andrew Pollington, Sanju Velani

For any $i, j \geq 0$ with $i + j = 1$ , let $\bad(i,j)$ denote the set of points $(x, y) \in R^{2}$ for which $max {∥ q x ∥^{1/ i}, ∥ q y ∥^{1/ j}} > c / q$ for all $q \in N$ . Here $c…