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

Pelegrí Viader, Jaume Paradís, Lluís Bibiloni

Research output: Contribution to journalArticleResearchpeer-review

40 Citations (Scopus)

Abstract

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. © 1998 Academic Press.
Original languageEnglish
Pages (from-to)212-227
JournalJournal of Number Theory
Volume73
Issue number2
DOIs
Publication statusPublished - 1 Dec 1998

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