The number of points from a random lattice that lie inside a ball

2013/11/12 by Holmin, Samuel
#11H06 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1311.2865

Abstract

We prove a sharp bound for the remainder term of the number of lattice points inside a ball, when averaging over a compact set of (not necessarily unimodular) lattices, in dimensions two and three. We also prove that such a bound cannot hold if one averages over the space of all lattices.

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