The exact order of the number of lattice points visible from the origin

2016/08/09 by Takeda, Wataru
#11N45 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1608.02703

Abstract

We say a lattice point X=(x₁,…,x_m) is visible from the origin, if gcd(x₁,...,x_m)=1. In other word, there are no other lattice point on the line segment from the origin O to X. From J.E. Nymann's result, we know that the number of lattice point from the origin in [-r,r]^m is (2r)^m/ζ(m)+(Error term). We showed that the exact order of the error term is r^m-1 for m≥3.

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