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Contribution to Book
Zero estimates for polynomials in 3 and 4 variables using orbits and stabilisers
Mathematics Faculty Works
  • Curtis Bennett, Loyola Marymount University
  • Lisa K. Elderbrock, Northern Kentucky University
  • Andrew M. W. Glass, Centre for Mathematical Sciences
Document Type
Book Chapter
Publication Date
12-1-2000
Disciplines
Abstract

To solve many Diophantine equations it often requires good lower bounds for linear forms in the logarithms of a small number of algebraic numbers. This in turn depends on good zero estimates: A non-zero polynomial cannot have a "grid" of zeros of size N unless it has large degree (in terms of N). Building on ideas of Wustholz (but using orbits and stabilisers) we obtain smaller bounds for the zero estimate for polynomials in 3 or 4 variables. We give an application to Catalan's conjecture.

Citation Information
C. Bennett, L. Elderbrock, & A.M.W. Glass, Zero-Estimates for Polynomials in 3 and 4 Variables using Orbits and Stabilizers, in Hilbert’s Tenth Problem: Relations with Arithmetic and Algebraic Geometry, AMS, 2000.