On the distribution of the convergents of almost all real numbers

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

Let n1 < n2 < ... be an infinite sequence of integers. The necessary and sufficient condition that for almost all α the inequality |α - ai ni| < ε{lunate} ni 2 with (ai, ni) = 1 should have infinitely many solutions is that Σi=1 φ{symbol}(ni) ni 2 = ∞. The techniques used in the proof can perhaps be applied to prove an old conjecture of Duffin and Schaeffer.

Original languageEnglish
Pages (from-to)425-441
Number of pages17
JournalJournal of Number Theory
Volume2
Issue number4
DOIs
Publication statusPublished - Nov 1970

ASJC Scopus subject areas

  • Algebra and Number Theory

Fingerprint Dive into the research topics of 'On the distribution of the convergents of almost all real numbers'. Together they form a unique fingerprint.

  • Cite this