arXiv subjects

Victoria Zhuravleva

Publications and source records attributed to Victoria Zhuravleva.

2 recordsLinked to original sources

arXiv2014

Diophantine approximations with Pisot numbers

Let $α$ be a Pisot number. Let $L(α)$ be the largest positive number such that for some $ξ=ξ(α)\in \mathbb R$ the limit points of the sequence of fractional parts $\{ξα^n\}_{n=1}^{\infty}$ all lie in the interval $[L(α), 1-L(α)]$. In this paper we show that if $α$ is of degree at most 4 or $α\le \frac{\sqrt 5 + 1}{2}$ then $L(α)\ge \frac{3}{17}$. Also we find explicitly the value of $L(α)$ for certain Pisot numbers of degree 3.

math.NT↗

arXiv2011

Diophantine approximations with Fibonacci numbers

Let $F_{n}$ be the $n$-th Fibonacci number. Put $φ=\frac{1+\sqrt5}{2}$. We prove that the following inequalities hold for any real $α$: 1) $\inf_{n \in \mathbb N} ||F_nα||\le\frac{φ-1}{φ+2}$, 2) $\liminf_{n\to \infty}||F_nα||\le 1/5$, 3) $\liminf_{n \to \infty}||φ^n α||\le 1/5$. These results are the best possible.

math.NT↗