N. A. Mironov

The Five Distance Theorem For An Arbitrary Norm

The three gap theorem states that the points of the Kronecker sequence $\alpha,2\alpha,\ldots,N\alpha$, considered modulo one, divide the circle into intervals of at most three distinct lengths. In a two-dimensional nearest-neighbour analogue, Haynes and Marklof proved that the Kronecker sequence modulo an arbitrary un...