Add to ORKGWe introduce two families of transcendental numbers which we call finite factorial (FF) and partially finite factorial (PFF) numbers respectively, with the former one being subfamily of the latter one. These numbers arise naturally from some transcendental criterion for real numbers via their $b$-ary expansions. We show that rational numbers (eventually periodic words) can not be finite factorial. Then we consider the geometric (topological) properties of the collection of all the FF numbers, including its countability, density and Hausdorff dimension. Some numerical examples are given to illustrate certain results in the work
Let b . 2 be an integer. We prove that the b-ary expansion of every irrational algebraic number cann...
AbstractWe prove a criterion for the transcendence of continued fractions whose partial quotients ar...
Rational functions have various kinds of finiteness. For instance, rational functions can be describ...
Is it possible to distinguish algebraic from transcendental real numbers by considering the $b$-ary ...
Let bgreater-or-equal, slanted2 be an integer. We prove that real numbers whose b-ary expansion sati...
It is widely believed that the continued fraction expansion of every irrational algebraic number $\a...
The aim of the present note is to establish two extensions of some transcendence criteria for real n...
AbstractWe apply the Ferenczi–Mauduit combinatorial condition obtained via a reformulation of Ridout...
Boris Adamczewski and Yann Bugeaud Let b ≥ 2 be an integer. We prove that the b-ary expansion of eve...
Real numbers are divided into rational and irrational numbers. Students learn about this division al...
Let $b \ge 2$ be an integer. We prove that the $b$-adic expansion of every irrational algebraic numb...
The continued fraction expansion of an irrational number $\alpha$ is eventually periodic if and only...
While the rational numbers Q are dense in the real numbers R, it seems like there are many, many mor...
We study some diophantine properties of automatic real numbers and we present a method to derive irr...
In the present work, we investigate real numbers whose sequence of partial quotients enjoys some com...
Let b . 2 be an integer. We prove that the b-ary expansion of every irrational algebraic number cann...
AbstractWe prove a criterion for the transcendence of continued fractions whose partial quotients ar...
Rational functions have various kinds of finiteness. For instance, rational functions can be describ...
Is it possible to distinguish algebraic from transcendental real numbers by considering the $b$-ary ...
Let bgreater-or-equal, slanted2 be an integer. We prove that real numbers whose b-ary expansion sati...
It is widely believed that the continued fraction expansion of every irrational algebraic number $\a...
The aim of the present note is to establish two extensions of some transcendence criteria for real n...
AbstractWe apply the Ferenczi–Mauduit combinatorial condition obtained via a reformulation of Ridout...
Boris Adamczewski and Yann Bugeaud Let b ≥ 2 be an integer. We prove that the b-ary expansion of eve...
Real numbers are divided into rational and irrational numbers. Students learn about this division al...
Let $b \ge 2$ be an integer. We prove that the $b$-adic expansion of every irrational algebraic numb...
The continued fraction expansion of an irrational number $\alpha$ is eventually periodic if and only...
While the rational numbers Q are dense in the real numbers R, it seems like there are many, many mor...
We study some diophantine properties of automatic real numbers and we present a method to derive irr...
In the present work, we investigate real numbers whose sequence of partial quotients enjoys some com...
Let b . 2 be an integer. We prove that the b-ary expansion of every irrational algebraic number cann...
AbstractWe prove a criterion for the transcendence of continued fractions whose partial quotients ar...
Rational functions have various kinds of finiteness. For instance, rational functions can be describ...