Assistant Professor of Mathematics Chad Awtrey and mathematics major Trevor Edwards published a research article in the current issue of International Journal of Pure and Applied Mathematics.
The article, “Dihedral p-adic fields of prime degree,” completely classifies all polynomials of prime degree with p-adic coefficients whose roots have a very special type of symmetry. This symmetry is encoded in the polynomial’s Galois group, and it can take on a number of different forms. The polynomials studied by Awtrey and Edwards are closely connected with symmetries of regular polygons. In this paper, Awtrey and Edwards determined the number of such polynomials for each prime degree as well as a finer description of the arithmetic properties of the corresponding fields.
This project is part of Awtrey’s ongoing research program in p-adic numbers, which has as its central mission to classify all extensions of the p-adic numbers by completely determining the arithmetic structure of their corresponding Galois groups. Such a task has merit, since the p-adic numbers are foundational to much of 20th and 21st century mathematics and are connected to many practical applications in physics, chemistry, and cryptography.
The complete citation of the article is:
Awtrey, Chad and Edwards, Trevor, Dihedral p-adic fields of prime degree, Int. J. Pure Appl. Math., 75, 185–194, 2012.