Nombres transcendants et répartition modulo 1
Non literal tranducers and some problems of normality
A new proof of Maxfield’s theorem is given, using automata and results from Symbolic Dynamics. These techniques permit to prove that points that are near normality to base (resp. ) are also near normality to base (resp. ), and to study genericity preservation for non Lebesgue measures when going from one base to the other. Finally, similar results are proved to bases the golden mean and its square.
Noncontinuable power series
Non-normality of continued fraction partial quotients modulo q
Nonoverlapping Pairs of Explicit Inversive Congruential Pseudorandom Numbers.
Non-primes are recursively divisible.
Normal number constructions for Cantor series with slowly growing bases
Let be a sequence of bases with . In the case when the are slowly growing and satisfy some additional weak conditions, we provide a construction of a number whose -Cantor series expansion is both -normal and -distribution normal. Moreover, this construction will result in a computable number provided we have some additional conditions on the computability of , and from this construction we can provide computable constructions of numbers with atypical normality properties.
Normal numbers and the Borel hierarchy
We show that the set of absolutely normal numbers is Π⁰₃-complete in the Borel hierarchy of subsets of real numbers. Similarly, the set of absolutely normal numbers is Π⁰₃-complete in the effective Borel hierarchy.
Normal numbers and the middle prime factor of an integer
Let pₘ(n) stand for the middle prime factor of the integer n ≥ 2. We first establish that the size of log pₘ(n) is close to √(log n) for almost all n. We then show how one can use the successive values of pₘ(n) to generate a normal number in any given base D ≥ 2. Finally, we study the behavior of exponential sums involving the middle prime factor function.
Normal recurring decimals, normal periodic systems, (j,ε) - normality, and normal numbers
Normalität bezüglich Matrizen.
Normality of numbers generated by the values of polynomials at primes
Note on a conjecture of P. D. T. A. Elliott
Note on Irregularities of Distibution.
Number theoretic expansions, algorithms and metrical observations.
Number theory, balls in boxes, and the asymptotic uniqueness of maximal discrete order statistics.
Od funkcí periodických ke skoroperiodickým
Odometers and systems of numeration
On a class of arithmetical sets
On a class of uniformly distributed sequences