N. Sidorov

activity

19962022

most citedExpansions in non-integer bases: lower, middle and top orders

66 citations · 329 across the 36 of their papers we have counts for

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7 papers · 1 filter

math.NT2020★ 6 cited

Conjugates of Pisot numbers

Kevin G. Hare, Nikita Sidorov

In this paper we investigate the Galois conjugates of a Pisot number $q \in (m, m + 1)$ , $m \geq 1$ . In particular, we conjecture that for $q \in (1, 2)$ we have $|q'| \geq \frac{\sqr…

math.NT2013★ 1 cited

Expansions in non-integer bases: lower order revisited

Simon Baker, Nikita Sidorov

Let $q \in (1, 2)$ and $x \in [0, \frac{1}{q - 1}]$ . We say that a sequence $(ε_{i})_{i = 1}^{\infty} \in {0, 1}^{N}$ is an expansion of $x$ in base $q$ (or a $q$ -expansion) if…

math.NT2009★ 7 cited

On the topology of sums in powers of an algebraic number

Nikita Sidorov, Boris Solomyak

Let $1 < q < 2$ and \[ Λ(q)={\sum_{k=0}^n a_kq^k\mid a_k\in\{-1,0,1\}, n\ge1}. \] It is well known that if $q$ is not a root of a polynomial with coefficients $0, \pm 1$ , then $Λ (q)$ is…

math.NT2009

Growth rate for beta-expansions

De-Jun Feng, Nikita Sidorov

Let $β > 1$ and let $m>\be$ be an integer. Each $x\in I_\be:=[0,\frac{m-1}{β-1}]$ can be represented in the form \[ x=\sum_{k=1}^\infty ε_kβ^{-k}, \] where $ε_{k} \in {0, 1, ..., m - 1}$ fo…

math.NT2006★ 66 cited

Expansions in non-integer bases: lower, middle and top orders

Nikita Sidorov

Let $q \in (1, 2)$ ; it is known that each $x \in [0, 1/ (q - 1)]$ has an expansion of the form $x = \sum_{n = 1}^{\infty} a_{n} q^{- n}$ with $a_{n} \in {0, 1}$ . It was shown in \cite{EJK} that if $q<(\…

math.NT2004

On the Gibbs properties of Bernoulli convolutions related to $β$ -numeration in multinacci bases

Eric Olivier, Nikita Sidorov, Alain Thomas

We consider infinitely convolved Bernoulli measures (or simply Bernoulli convolutions) related to the $β$ -numeration. A matrix decomposition of these measures is obtained in the ca…