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A New Light on Minkowski's ?(x) Function

✍ Scribed by Pelegrı́ Viader; Jaume Paradı́s; Lluı́s Bibiloni

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
322 KB
Volume
73
Category
Article
ISSN
0022-314X

No coin nor oath required. For personal study only.

✦ Synopsis

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. The singularity of ?(x) is 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 vice versa. These sets are described by means of metrical properties of different systems for real number representation.

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