Zobrazeno 1 - 10
of 91
pro vyhledávání: '"Badziahin, Dzmitry"'
Autor:
Badziahin, Dzmitry
We compute the Hausdorff dimension of the set of simultaneously $q^{-\lambda}$-well approximable points on the Veronese curve in $\mathbb{R}^n$ for $\lambda$ between $\frac{1}{n}$ and $\frac{2}{2n-1}$. For $n=3$, the same result is given for a wider
Externí odkaz:
http://arxiv.org/abs/2403.17685
Autor:
Badziahin, Dzmitry
We provide an upper bound on the efficient irrationality exponents of cubic algebraics $x$ with the minimal polynomial $x^3 - tx^2 - a$. In particular, we show that it becomes non-trivial, i.e. better than the classical bound of Liouville in the case
Externí odkaz:
http://arxiv.org/abs/2301.02391
Publikováno v:
Proc. Edinb. Math. Soc. 64, no. 2 (2021), 317-337
Let $p$ be a prime number. For a positive integer $n$ and a real number $\xi$, let $\lambda_n (\xi)$ denote the supremum of the real numbers $\lambda$ for which there are infinitely many integer tuples $(x_0, x_1, \ldots , x_n)$ such that $| x_0 \xi
Externí odkaz:
http://arxiv.org/abs/2007.14785
Autor:
Badziahin, Dzmitry
We consider a Laurent series defined by infinite products $g_u(t) = \prod_{n=0}^\infty (1 + ut^{-2^n})$, where $u\in \mathbb{F}$ is a parameter and $\mathbb{F}$ is a field. We show that for all $u\in\mathbb{Q}\setminus\{-1,0,1\}$ the series $g_u(t)$
Externí odkaz:
http://arxiv.org/abs/2001.01422
We improve the lower bound for the classical exponent of approximation $w_{n}^{\ast}(\xi)$ connected to Wirsing's famous problem of approximation to real numbers by algebraic numbers of degree at most $n$. Our bound exceeds $n/\sqrt{3}\approx 0.5773n
Externí odkaz:
http://arxiv.org/abs/1912.09013
Akademický článek
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Autor:
Badziahin, Dzmitry
We consider Mahler functions $f(z)$ which solve the functional equation $f(z) = \frac{A(z)}{B(z)} f(z^d)$ where $\frac{A(z)}{B(z)}\in \mathbb{Q}(z)$ and $d\ge 2$ is integer. We prove that for any integer $b$ with $|b|\ge 2$ either $f(b)$ is rational
Externí odkaz:
http://arxiv.org/abs/1806.02946
Schmidt games and the Cantor winning property give alternative notions of largeness, similar to the more standard notions of measure and category. Being intuitive, flexible, and applicable to recent research made them an active object of study. We su
Externí odkaz:
http://arxiv.org/abs/1804.06499
Autor:
Badziahin, Dzmitry, Zorin, Evgeniy
We provide a non-trivial measure of irrationality for a class of Mahler numbers defined with infinite products which cover the Thue-Morse constant.
Comment: 24 pages
Comment: 24 pages
Externí odkaz:
http://arxiv.org/abs/1707.06677
Akademický článek
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