On the extremal theory of continued fractions

Alina Bazarova, István Berkes, Lajos Horváth

Research output: Contribution to journalArticlepeer-review


Letting (Formula presented.) denote the continued fraction expansion of an irrational number (Formula presented.) , Khinchin proved that (Formula presented.) in measure, but not for almost every (Formula presented.). Diamond and Vaaler showed that, removing the largest term from (Formula presented.) , the previous asymptotics will hold almost everywhere, this shows the crucial influence of the extreme terms of (Formula presented.) on the sum. In this paper we determine, for (Formula presented.) and (Formula presented.) , the precise asymptotics of the sum of the (Formula presented.) largest terms of (Formula presented.) and show that the sum of the remaining terms has an asymptotically Gaussian distribution.
Original languageEnglish
Pages (from-to)248-266
JournalJournal of Theoretical Probability
Issue number1
Publication statusPublished - 2016

Fields of Expertise

  • Information, Communication & Computing

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)


Dive into the research topics of 'On the extremal theory of continued fractions'. Together they form a unique fingerprint.

Cite this