The asymptotic properties of ϕ(n) and a problem related to visibility of Lattice points

2017/10/28 by Debmalya Basak, Basak, Debmalya
Mathematics · Arts and Humanities · #Analytic Number Theory Research #Mathematical Dynamics and Fractals #Historical Studies and Socio-cultural Analysis

paper · pdf · doi:10.48550/arxiv.1710.10517

Abstract

We look at the average sum of the Euler's phi function ϕ(n) and it's relation with the visibility of a point from the origin.We show that ∀\hspace0.05ink ≥1,k∈ℕ,∃ a k\timesk grid in the 2D space such that no point inside it is visible from the origin.We define visibility of a lattice point from a set and try to find a bound for the cardinality of the smallest set S such that for a given n ∈ℕ,all points from the n\timesn grid are visible from S.

Related

• Visible lattice points along curves
• Lattice point visibility on power functions
• The exact order of the number of lattice points visible from the origin
• On the density of visible lattice points along polynomials
• Non-Euclidean visibility problems