Borel conjectured that all algebraic irrational numbers are normal in base 2. However, very little is known about this problem. We improve the lower bounds for the number of digit changes in the binary expansions of algebraic irrational numbers
We give metric theorems for the property of Borel normality for real numbers under the assumption o...
Employing concepts from additive number theory, together with results on binary evaluations and part...
For an integer b ≥ 2 a real number α is b -normal if, for all m > 0, every m-long string of digits i...
Abstract. Let Bn(x) denote the number of 1’s occuring in the binary expansion of an irrational numbe...
This thesis studies some links between the combinatorial properties of the base-b expansion or of th...
Abstract. Classical ways to represent a real number are by its continued fraction ex-pansion or by i...
Boris Adamczewski and Yann Bugeaud Let b ≥ 2 be an integer. We prove that the b-ary expansion of eve...
The main goal of this work is to give a lower bound to the number of digit changes in the beta-expa...
Let $b \ge 2$ be an integer. We prove that the $b$-adic expansion of every irrational algebraic numb...
We deduce the transcendence of the Iwasawa power series from Borel's conjecture, namely, the no...
Let b . 2 be an integer. We prove that the b-ary expansion of every irrational algebraic number cann...
Let r, g ≥ 2 be integers such that log g/log r is irrational. We show that under r-digitwise random ...
International audience— We consider the complexity of integer base expansions of algebraic irrationa...
In this paper we consider representation of numbers in an irrational basis β> 1. We study the ari...
A number is normal to the base r if, in its expansion to that base, all possible digit strings of le...
We give metric theorems for the property of Borel normality for real numbers under the assumption o...
Employing concepts from additive number theory, together with results on binary evaluations and part...
For an integer b ≥ 2 a real number α is b -normal if, for all m > 0, every m-long string of digits i...
Abstract. Let Bn(x) denote the number of 1’s occuring in the binary expansion of an irrational numbe...
This thesis studies some links between the combinatorial properties of the base-b expansion or of th...
Abstract. Classical ways to represent a real number are by its continued fraction ex-pansion or by i...
Boris Adamczewski and Yann Bugeaud Let b ≥ 2 be an integer. We prove that the b-ary expansion of eve...
The main goal of this work is to give a lower bound to the number of digit changes in the beta-expa...
Let $b \ge 2$ be an integer. We prove that the $b$-adic expansion of every irrational algebraic numb...
We deduce the transcendence of the Iwasawa power series from Borel's conjecture, namely, the no...
Let b . 2 be an integer. We prove that the b-ary expansion of every irrational algebraic number cann...
Let r, g ≥ 2 be integers such that log g/log r is irrational. We show that under r-digitwise random ...
International audience— We consider the complexity of integer base expansions of algebraic irrationa...
In this paper we consider representation of numbers in an irrational basis β> 1. We study the ari...
A number is normal to the base r if, in its expansion to that base, all possible digit strings of le...
We give metric theorems for the property of Borel normality for real numbers under the assumption o...
Employing concepts from additive number theory, together with results on binary evaluations and part...
For an integer b ≥ 2 a real number α is b -normal if, for all m > 0, every m-long string of digits i...
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