TY - JOUR

T1 - The three gap theorem and the space of lattices

AU - Marklof, Jens

AU - Strombergsson, Andreas

PY - 2017/10

Y1 - 2017/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85032619352&partnerID=8YFLogxK

U2 - 10.4169/amer.math.monthly.124.8.741

DO - 10.4169/amer.math.monthly.124.8.741

M3 - Article (Academic Journal)

AN - SCOPUS:85032619352

VL - 124

SP - 741

EP - 745

JO - American Mathematical Monthly

JF - American Mathematical Monthly

SN - 0002-9890

IS - 8

ER -