Short proofs of theorems of Lekkerkerker and Ballieu

Max Riederle

International Journal of Mathematics and Mathematical Sciences, 1982, vol. 5, 1-4

Abstract:

For any irrational number ξ let A ( ξ ) denote the set of all accumulation points of { z : z = q ( q ξ − p ) , p ∈ ℤ , q ∈ ℤ − { 0 } , p and q relatively prime } . In this paper the following theorem of Lekkerkerker is proved in a short and elementary way: The set A ( ξ ) is discrete and does not contain zero if and only if ξ is a quadratic irrational. The procedure used for this proof simultaneously takes care of a theorem of Ballieu.

Date: 1982
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/5/159839.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/5/159839.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:159839

DOI: 10.1155/S0161171282000581

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().