The Igusa local zeta function for $x^n+y^m$

TL;DR

This paper investigates the Igusa local zeta function for the algebraic curves defined by x^n + y^m, providing specific calculations, an introduction to p-adic analysis, and discussing various computational methods.

Contribution

It offers new explicit results for the Igusa local zeta function of x^n + y^m and reviews methods used in p-adic analysis for such computations.

Findings

Explicit formulas for the zeta function of x^n + y^m

Comparison of computational methods in p-adic analysis

Introduction to p-adic analysis techniques

Abstract

This paper provides specific results on the Igusa local zeta function for the curves $x^n+y^m$. In addition to specific results, we give an introduction to $p$-adic analysis and a discussion of various methods which have been used to compute these zeta functions. The paper was written by the 1992 REU group in $p$-adic analysis supervised by Margaret Robinson. It has been available on the Mount Holyoke REU website.