Cantor series constructions of sets of normal numbers
Characterizations of Midy's property.
Characterizing Frobenius semigroups by filtration.
Combinatorial and arithmetical properties of infinite words associated with non-simple quadratic Parry numbers
We study some arithmetical and combinatorial properties of β-integers for β being the larger root of the equation x2 = mx - n,m,n ∈ ℵ, m ≥ n +2 ≥ 3. We determine with the accuracy of ± 1 the maximal number of β-fractional positions, which may arise as a result of addition of two β-integers. For the infinite word uβ> coding distances between the consecutive β-integers, we determine precisely also the balance. The word uβ> is the only fixed point of the morphism A → Am-1B and B → Am-n-1B. In...
Comments on the height reducing property
A complex number α is said to satisfy the height reducing property if there is a finite subset, say F, of the ring ℤ of the rational integers such that ℤ[α] = F[α]. This property has been considered by several authors, especially in contexts related to self affine tilings and expansions of real numbers in non-integer bases. We prove that a number satisfying the height reducing property, is an algebraic number whose conjugates, over the field of the rationals, are all of modulus one, or all of modulus...
Completely q-multiplicative functions: the Mellin transform approach
Complexity of infinite words associated with beta-expansions
We study the complexity of the infinite word associated with the Rényi expansion of in an irrational base . When is the golden ratio, this is the well known Fibonacci word, which is sturmian, and of complexity . For such that is finite we provide a simple description of the structure of special factors of the word . When we show that . In the cases when or we show that the first difference of the complexity function takes value in for every , and consequently we determine...
Complexity of infinite words associated with beta-expansions
We study the complexity of the infinite word uβ associated with the Rényi expansion of 1 in an irrational base β > 1. When β is the golden ratio, this is the well known Fibonacci word, which is Sturmian, and of complexity C(n) = n + 1. For β such that dβ(1) = t1t2...tm is finite we provide a simple description of the structure of special factors of the word uβ. When tm=1 we show that C(n) = (m - 1)n + 1. In the cases when t1 = t2 = ... tm-1or t1 > max{t2,...,tm-1} we show that the first difference of...
Computo del numero delle coppie di numeri primi gemelli comprese tra e , distinte secondo le cifre terminali.
Construction of normal numbers via pseudo-polynomial prime sequences
We construct normal numbers in base q by concatenating q-ary expansions of pseudo-polynomials evaluated at primes. This extends a recent result by Tichy and the author.
Continued fractions for some algebraic numbers.
Corrigendum : “Complexity of infinite words associated with beta-expansions”
We add a sufficient condition for validity of Propo- sition 4.10 in the paper Frougny et al. (2004). This condition is not a necessary one, it is nevertheless convenient, since anyway most of the statements in the paper Frougny et al. (2004) use it.
Corrigendum: Complexity of infinite words associated with beta-expansions
We add a sufficient condition for validity of Propo- sition 4.10 in the paper Frougny et al. (2004). This condition is not a necessary one, it is nevertheless convenient, since anyway most of the statements in the paper Frougny et al. (2004) use it.
Counting Keith numbers.
Counting optimal joint digit expansions.