Functiones et Approximatio Commentarii Mathematici

Construction of normal numbers by classified prime divisors of integers II

Jean-Marie De Koninck and Imre Kátai

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Abstract

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.

Article information

Source
Funct. Approx. Comment. Math., Volume 49, Number 1 (2013), 7-27.

Dates
First available in Project Euclid: 20 September 2013

Permanent link to this document
https://projecteuclid.org/euclid.facm/1379686431

Digital Object Identifier
doi:10.7169/facm/2013.49.1.1

Mathematical Reviews number (MathSciNet)
MR2895156

Zentralblatt MATH identifier
1283.11109

Subjects
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

Keywords
normal numbers primes arithmetic function

Citation

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


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References

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  • J.M. De Koninck and I. Kátai, Construction of normal numbers by classified prime divisors of integers, Functiones et Approximatio 45.2 (2011), 231–253.
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