Are there any nice estimates for the size of the largest disc (centered anywhere) not intersecting a unimodular (i.e. covolume = 1) lattice in the plane? Maybe estimates in terms of the shortest nonzero vector in the lattice. I know absolutely nothing about the geometry of numbers, so please forgive my naivete.
2026-03-26 12:34:48.1774528488
estimates for the largest disc not intersecting a unimodular lattice?
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called covering radius. not dependent on unimodularity. If any full-dimensional ball of radius $r$ contains a lattice point, then the union of balls of radius $r$ centered at all lattice points contains all points of the vector space