Searching for Rigidity in Algebraic Starscapes

Abstract

We create plots of algebraic integers in the complex plane, exploring the effect of sizing the integers according to various arithmetic invariants. We focus on Galois theoretic invariants, in particular creating plots which emphasize algebraic integers whose Galois group is not the full symmetric group--these integers we call rigid. We then give some analysis of the resulting images, suggesting avenues for future research about the geometry of so-called rigid algebraic integers.

17 Pages, 5 figures and 2 tables, including 13 full color images. Update includes a new result (Proposition 4.1). To appear in the Journal of Mathematics and the Arts