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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

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.