Comptes Rendus
Number theory
Exceptional parameters of linear mod one transformations and fractional parts {ξ(p/q)n}
[Paramètres exceptionnels de transformations linéaires mod un et parties fractionnaires {ξ(p/q)n}]
Comptes Rendus. Mathématique, Volume 353 (2015) no. 4, pp. 291-296.

Nous étudions des paramètres exceptionnels de transformations linéaires mod un. La présente note prouve que l'ensemble de ces valeurs a zéro pour dimension de Hausdorff. Ceci répond à la question posée par Bugeaud.

We study exceptional parameters of linear mod one transformations. The present note proves that the set of such values has Hausdorff dimension zero. This answers the question posed by Bugeaud.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.01.017

DoYong Kwon 1

1 Department of Mathematics, Chonnam National University, Gwangju 500-757, Republic of Korea
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DoYong Kwon. Exceptional parameters of linear mod one transformations and fractional parts $ \{\xi {(p/q)}^{n}\}$. Comptes Rendus. Mathématique, Volume 353 (2015) no. 4, pp. 291-296. doi : 10.1016/j.crma.2015.01.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.01.017/

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[6] G.H. Hardy; E.M. Wright An Introduction to the Theory of Numbers, Oxford University Press, Oxford, 2008

[7] D.Y. Kwon A devil's staircase from rotations and irrationality measures for Liouville numbers, Math. Proc. Camb. Philos. Soc., Volume 145 (2008) no. 3, pp. 739-756

[8] D.Y. Kwon The natural extensions of β-transformations which generalize Baker's transformations, Nonlinearity, Volume 22 (2009) no. 2, pp. 301-310

[9] D.Y. Kwon The orbit of a β-transformation cannot lie in a small interval, J. Korean Math. Soc., Volume 49 (2012) no. 4, pp. 867-879

[10] D.Y. Kwon Moments of discrete measures with dense jumps induced by β-expansions, J. Math. Anal. Appl., Volume 399 (2013) no. 1, pp. 1-11

[11] D.Y. Kwon A two-dimensional singular function via Sturmian words in base β, J. Number Theory, Volume 133 (2013) no. 11, pp. 3982-3994

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