JournalsrlmVol. 28, No. 1pp. 65–83

On the analytic bijections of the rationals in [0,1]

  • Davide Lombardo

    Université Paris-Sud, Orsay, France
On the analytic bijections of the rationals in [0,1] cover
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Abstract

We carry out an arithmetical study of analytic functions f:[0,1][0,1]f: [0,1] \to [0,1] that by restriction induce a bijection Q[0,1]Q[0,1]\mathbb{Q} \cap [0,1] \to \mathbb{Q} \cap [0,1]. The existence of such functions shows that, unless f(x)f(x) has some additional property of an algebraic nature, very little can be said about the distribution of rational points on its graph. Some more refined questions involving heights are also explored.

Cite this article

Davide Lombardo, On the analytic bijections of the rationals in [0,1]. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 28 (2017), no. 1, pp. 65–83

DOI 10.4171/RLM/752