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Publication - Professor Jens Marklof

    The three gap theorem and the space of lattices


    Marklof, J & Strombergsson, A, 2017, ‘The three gap theorem and the space of lattices’. American Mathematical Monthly, vol 124., pp. 741-745


    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.

    Full details in the University publications repository