## Functiones et Approximatio Commentarii Mathematici

### Two exceptional classes of real numbers

Purusottam Rath

#### Abstract

In a recent paper, Bugeaud and Dubickas have given an explicit characterisation of a rather remarkable class of transcendental numbers which are exceptional from the perspective of distribution of exponential sequences modulo $1$. Muchbefore, Helson and Kahane, from a completely different point-of-view hadexistentially exhibited another class of exceptional real numbers which conjecturally are either rational or transcendental. Wondering whether these two rather large class of real numbers overlap, we study their distribution functions and our investigation gives the first indication that these two interesting class of real numbers originating from different contexts are most likely different. We also frame a natural conjecture in this set up which would establish the above assertion. Our results can be regarded as the first step towards this conjecture.

#### Article information

Source
Funct. Approx. Comment. Math., Volume 38, Number 1 (2008), 81-91.

Dates
First available in Project Euclid: 18 December 2008

https://projecteuclid.org/euclid.facm/1229624653

Digital Object Identifier
doi:10.7169/facm/1229624653

Mathematical Reviews number (MathSciNet)
MR2433790

Zentralblatt MATH identifier
1231.11085

Subjects
Secondary: 11K31: Special sequences

#### Citation

Rath, Purusottam. Two exceptional classes of real numbers. Funct. Approx. Comment. Math. 38 (2008), no. 1, 81--91. doi:10.7169/facm/1229624653. https://projecteuclid.org/euclid.facm/1229624653

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