Add to ORKGA real number alpha is said to be b-normal if every m-long string of digits appears in the base-b expansion of alpha with limiting frequency b-m. We prove that alpha is b-normal if and only if it possesses no base-b "hot spot." In other words, alpha is b-normal if and only if there is no real number y such that smaller and smaller neighborhoods of y are visited by the successive shifts of the base-b expansion of alpha with larger and larger frequencies, relative to the lengths of these neighborhood
It is shown that, under the action of random digitwise decaying perturbations not changing the spect...
In 1914, Felix Hausdorff published an elegant proof that almost all numbers are simply normal in bas...
Borel conjectured that all algebraic irrational numbers are normal in base 2. However, very little i...
A number is normal to the base r if, in its expansion to that base, all possible digit strings of le...
This paper discusses discusses a certain mathematical constant that was recently proven to be 2-norm...
For an integer b ≥ 2 a real number α is b -normal if, for all m > 0, every m-long string of digits i...
We give metric theorems for the property of Borel normality for real numbers under the assumption o...
It is widely believed that several fundamental mathematical constants, like pi, e, log 2 and so on, ...
Let s be an integer greater than or equal to 2. A real number is simply normal to base s if in its b...
Let b ≥ 2 be an integer. A real number is called simply normal to base b if in its representation to...
Graduation date: 2012The notion of a normal number and the Normal Number Theorem date back over 100 ...
It is shown that every optimal binary code with covering radius R=1 is normal. This (parity) proves ...
Let r, g ≥ 2 be integers such that log g/log r is irrational. We show that under r-digitwise random ...
AbstractThe set L of essentially non-normal numbers of the unit interval (i.e., the set of real numb...
We use probabilistic methods, along with other techniques, to address three topics in number theory ...
It is shown that, under the action of random digitwise decaying perturbations not changing the spect...
In 1914, Felix Hausdorff published an elegant proof that almost all numbers are simply normal in bas...
Borel conjectured that all algebraic irrational numbers are normal in base 2. However, very little i...
A number is normal to the base r if, in its expansion to that base, all possible digit strings of le...
This paper discusses discusses a certain mathematical constant that was recently proven to be 2-norm...
For an integer b ≥ 2 a real number α is b -normal if, for all m > 0, every m-long string of digits i...
We give metric theorems for the property of Borel normality for real numbers under the assumption o...
It is widely believed that several fundamental mathematical constants, like pi, e, log 2 and so on, ...
Let s be an integer greater than or equal to 2. A real number is simply normal to base s if in its b...
Let b ≥ 2 be an integer. A real number is called simply normal to base b if in its representation to...
Graduation date: 2012The notion of a normal number and the Normal Number Theorem date back over 100 ...
It is shown that every optimal binary code with covering radius R=1 is normal. This (parity) proves ...
Let r, g ≥ 2 be integers such that log g/log r is irrational. We show that under r-digitwise random ...
AbstractThe set L of essentially non-normal numbers of the unit interval (i.e., the set of real numb...
We use probabilistic methods, along with other techniques, to address three topics in number theory ...
It is shown that, under the action of random digitwise decaying perturbations not changing the spect...
In 1914, Felix Hausdorff published an elegant proof that almost all numbers are simply normal in bas...
Borel conjectured that all algebraic irrational numbers are normal in base 2. However, very little i...