The three gap theorem and the space of lattices

2016/12/15 by Marklof, Jens, Strömbergsson, Andreas · 2 citations
#11H06 #11J71 #52C05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1612.04906

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.

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