N. Sidorov

collaborators

3 papers

math.CA2023

Bernoulli convolutions -- 2023

Nikita Sidorov

Let $θ \in (1, 2)$ , and $μ_{θ}$ be the Bernoulli convolution parametrized by $θ$ , that is, the measure corresponding to the distribution of the random variable $\sum_{n=1}^{\infty} a_nθ…

math.DS2023

Complex dimensions for IFS with overlaps

Nikita Sidorov

The notion of complex dimension of a one-dimensional Cantor set $C = ⋂_{n = 1}^{\infty} C_{n}$ dates back decades. It is defined as the set of poles of the meromorphic $ζ$ -function $…

math.NT2023

On some properties of Perron numbers

Nikita Sidorov

Let $θ$ be a real number, $n \in N$ , and $D_{n} (θ) = {\sum_{k = 1}^{n} a_{k} θ^{k} ∣ a_{k} \in {0, \dots, ⌊ θ ⌋}} .$ Let $θ$ be a Perron number, that is, an algebr…