Ternary Diophantine Equations via Galois Representations and Modular Forms

Michael A. Bennett, Chris M. Skinner

Research output: Contribution to journalArticle

110 Scopus citations

Abstract

In this paper, we develop techniques for solving ternary Diophantine equations of the shape Axn + Byn = Cz2, based upon the theory of Galois representations and modular forms. We subsequently utilize these methods to completely solve such equations for various choices of the parameters A, B and C. We conclude with an application of our results to certain classical polynomial-exponential equations, such as those of Ramanujan-Nagell type.

Original languageEnglish (US)
Pages (from-to)23-54
Number of pages32
JournalCanadian Journal of Mathematics
Volume56
Issue number1
DOIs
StatePublished - Feb 2004
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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