We carry out an arithmetical study of analytic functions f:[0,1]→[0,1] that by restriction induce a bijection Q∩[0,1]→Q∩[0,1]. The existence of such functions shows that, unless 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.
On the analytic bijections of the rationals in [0,1]
LOMBARDO, DAVIDE
2017-01-01
Abstract
We carry out an arithmetical study of analytic functions f:[0,1]→[0,1] that by restriction induce a bijection Q∩[0,1]→Q∩[0,1]. The existence of such functions shows that, unless 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.File in questo prodotto:
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