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We carry out an arithmetical study of analytic functions that by restriction induce a bijection . The existence of such functions shows that, unless 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. 65–83DOI 10.4171/RLM/752