Functiones et Approximatio Commentarii Mathematici
- Funct. Approx. Comment. Math.
- Volume 49, Number 1 (2013), 7-27.
Construction of normal numbers by classified prime divisors of integers II
Given an integer $q\ge 2$, a $q$-normal number is an irrational number $\eta$ such that any preassigned sequence of $k$ digits occurs in the $q$-ary expansion of $\eta$ at the expected frequency, namely$1/q^k$. In a series of recent papers, using the complexity of the multiplicative structure of integers along with a method we developed in 1995 regarding the distribution of subsets of primes in the prime factorization of integers, we initiated new methods allowing for the creation of large families of normal numbers. Here, we further expand on this initiative.
Funct. Approx. Comment. Math., Volume 49, Number 1 (2013), 7-27.
First available in Project Euclid: 20 September 2013
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11K16: Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. [See also 11A63]
Secondary: 11N37: Asymptotic results on arithmetic functions 11A41: Primes
De Koninck, Jean-Marie; Kátai, Imre. Construction of normal numbers by classified prime divisors of integers II. Funct. Approx. Comment. Math. 49 (2013), no. 1, 7--27. doi:10.7169/facm/2013.49.1.1. https://projecteuclid.org/euclid.facm/1379686431