Back to Search Start Over

Construction of normal numbers by classified prime divisors of integers

Authors :
Jean-Marie De Koninck
Imre Kátai
Source :
Funct. Approx. Comment. Math. 45, no. 2 (2011), 231-253
Publication Year :
2011
Publisher :
Adam Mickiewicz University, Faculty of Mathematics and Computer Science, 2011.

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.

Details

Language :
English
Database :
OpenAIRE
Journal :
Funct. Approx. Comment. Math. 45, no. 2 (2011), 231-253
Accession number :
edsair.doi.dedup.....ca90de08dcba6bf5701e6ccfa718202d