Paper #226

Título:

A new light on Minkowski's? $(x)$ function

Autores:

Pelegrí Viader, Jaume Paradís y Lluís Bibiloni

Fecha:

Junio 1997

Resumen:

The well--known Minkowski's? $(x)$ function is presented as the asymptotic distribution function of an enumeration of the rationals in (0,1] based on their continued fraction representation. Besides, the singularity of ?$(x)$ is clearly proved in two ways: by exhibiting a set of measure one in which ?�$(x)$ = 0; and again by actually finding a set of measure one which is mapped onto a set of measure zero and viceversa. These sets are described by means of metrical properties of different systems for real number representation.

Palabras clave:

Asymptotic distribution functions, Minkowski's function, singular functions

Códigos JEL:

C00

Área de investigación:

Estadística, Econometría y Métodos Cuantitativos

Publicado en:

Journal of Number Theory, 73, (1998), pp. 212-227

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