Functiones et Approximatio Commentarii Mathematici

Kondo-Saito-Tanaka theorem

Jean-Marie De Koninck and Imre Kátai

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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 $1/q^k$. Given an integer $q\ge 3$, we consider the sequence of primes reduced modulo $q$ and examine various possibilities of constructing normal numbers using this sequence. We create a sequence of independent random variables that mimics the sequence of primes and then show that for almost all outcomes this allows to obtain a normal number.

Article information

Funct. Approx. Comment. Math., Volume 49, Number 2 (2013), 291-302.

First available in Project Euclid: 20 December 2013

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Mathematical Reviews number (MathSciNet)

Primary: 11K16: Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. [See also 11A63]
Secondary: 11N05: Distribution of primes 11B50: Sequences (mod $m$)

normal numbers primes


De Koninck, Jean-Marie; Kátai, Imre. Kondo-Saito-Tanaka theorem. Funct. Approx. Comment. Math. 49 (2013), no. 2, 291--302. doi:10.7169/facm/2013.49.2.8.

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