The density of visible points in the Ammann-Beenker point set

2018/03/17 by Hammarhjelm, Gustav
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1803.06481

Abstract

The relative density of visible points of the integer lattice ℤ^d is known to be 1/ζ(d) for d≥ 2, where ζ is Riemann's zeta function. In this paper we prove that the relative density of visible points in the Ammann-Beenker point set is given by 2(√(2)-1)/ζ_K(2), where ζ_K is Dedekind's zeta function over K=ℚ(√(2)).

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