The p-adic valuation of the general degree-2 and degree-3 polynomial in 2 variables

TL;DR

This paper studies the p-adic valuation trees of quadratic and cubic polynomials in two variables over any prime p, extending previous research to better understand their valuation structures.

Contribution

It introduces a comprehensive analysis of p-adic valuation trees for degree-2 and degree-3 polynomials in two variables, expanding the theoretical framework in this area.

Findings

Characterization of p-adic valuation trees for quadratic polynomials

Extension of valuation tree analysis to cubic polynomials

Generalization to polynomials over any prime p

Abstract

This paper investigates the p-adic valuation trees of degree-2 and degree-3 polynomials in two variables over any prime p, building upon prior research outlined in [14].