Generalized Lattice Point Visibility

An integer lattice point is said to be visible if a direct line of sight from the origin can be drawn to it. Visible and invisible lattice points can be classified by the greatest common divisor (gcd) of their components. If we instead consider curved lines of sight, the standard gcd is no longer sufficient to classify lattice point visibility. In this talk we discuss properties of a generalized gcd called the weighted greatest common divisor (wgcd) and how it can be used to classify lattice point visibility along parameterized curves in higher dimensions.