The three gap theorem and the space of lattices

Jens Marklof, Andreas Strombergsson

Research output: Contribution to journalArticle (Academic Journal)peer-review

8 Citations (Scopus)
235 Downloads (Pure)

Abstract

The three gap theorem (or Steinhaus conjecture) asserts that there are at most three distinct gap lengths in the fractional parts of the sequence α, 2α, ⋯, Nα, for any integer N and real number α. This statement was proved in the 1950s independently by various authors. Here we present a different approach using the space of two-dimensional Euclidean lattices.
Original languageEnglish
Pages (from-to)741-745
Number of pages5
JournalAmerican Mathematical Monthly
Volume124
Issue number8
Early online date1 Oct 2017
DOIs
Publication statusPublished - Oct 2017

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