Dmitry Badziahin

activity

20092022

most citedOn the complexity of a putative counterexample to the

p

-adic Littlewood conjecture

12 citations · 12 across the 5 of their papers we have counts for

collaborators

6 papers

math.NT2022

Badly approximable infinite products of quadratic polynomials

Dmitry Badziahin, Cameron Eggins

We provide a number of conditions on the rational numbers $u$ and $v$ which ensure that the Laurent series $g_{u, v} (x) := \prod_{t = 0}^{\infty} (1 + u x^{- 3^{t}} + v x^{- 2 \cdot 3^{t}})$ is badl…

math.NT2022

Continued fractions of cubic Laurent series

Dmitry Badziahin

We construct continued fraction expansions for several families of the Laurent series in $Q [[t^{- 1}]]$ . To the best of the author's knowledge, this is the first result of…

math.NT2020

Badly approximable numbers, Kronecker's theorem, and diversity of Sturmian characteristic sequences

Dmitry Badziahin, Jeffrey Shallit

We give an optimal version of the classical ``three-gap theorem'' on the fractional parts of $n θ$ , in the case where $θ$ is an irrational number that is badly approximable. As a c…

math.NT2017

Continued fractions of certain Mahler functions

Dmitry Badziahin

We investigate the continued fraction expansion of the infinite products $g (x) = x^{- 1} \prod_{t = 0}^{\infty} P (x^{- d^{t}})$ where polynomials $P (x)$ satisfy $P (0) = 1$ and $° (P) < d$ . We co…

math.NT2014★ 12 cited

On the complexity of a putative counterexample to the $p$ -adic Littlewood conjecture

Dmitry Badziahin, Yann Bugeaud, Manfred Einsiedler +1

Let $∣∣ \cdot ∣∣$ denote the distance to the nearest integer and, for a prime number $p$ , let $∣ \cdot ∣_{p}$ denote the $p$ -adic absolute value. In 2004, de Mathan and Teulié asked…

math.NT2009

A note on Farey fractions with denominators in arithmetic progressions

Dmitry A. Badziahin, Alan K. Haynes

As the conclusion of a line of investigation undertaken in two previous papers, we compute asymptotic frequencies for the values taken by numerators of differences of consecutive F…

Badly approximable infinite products of quadratic polynomials

Continued fractions of cubic Laurent series

Badly approximable numbers, Kronecker's theorem, and diversity of Sturmian characteristic sequences

Continued fractions of certain Mahler functions

On the complexity of a putative counterexample to the p-adic Littlewood conjecture

A note on Farey fractions with denominators in arithmetic progressions

On the complexity of a putative counterexample to the $p$ -adic Littlewood conjecture