Work

Products of p-Adic Valuation Trees

Year: 2024

Type: article

Abstract: The study of prime divisibility plays a crucial role in number theory. The p-adic valuation of a number is the highest power of a prime, p, that divides that number. Using this valuation, we construct p-adic valuation trees to visually represent the valuations of a sequence. We investigate how nodes split on trees generated by linear functions with rational coefficients, as well as those formed from a product of linear or lower degree polynomials. We describe the infinite branches of these polynomial trees and the valuations of their terminating nodes.

Source: The PUMP Journal of Undergraduate Research

DOI: 10.46787/pump.v7i0.3877

Author: Dillon Snyder

Institution: University of Connecticut

Language: English

Topic: advanced mathematical theories

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Award: REU SITE: Exploration and Professional Excellence in the Mathematical Sciences