Thomas' family of thue equations over imaginary quadratic fields

Clemens Heuberger, Attila Petho, Robert F. Tichy

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

We consider the family of relative Thue equations x3 - (t - 1)x2y - (t + 2)xy2 - y3 = μ, where the parameter t, the root of unity μ and the solutions x and y are integers in the same imaginary quadratic number field. We prove that there are only trivial solutions (with x , y ≤ 1), if t is large enough or if the discriminant of the quadratic number field is large enough or if Ret = -1/2 (there are a few more solutions in this case which are explicitly listed). In the case Ret = -1/2, an algebraic method is used, in the general case, Baker's method yields the result.

Original languageEnglish
Pages (from-to)437-449
Number of pages13
JournalJournal of Symbolic Computation
Volume34
Issue number5
DOIs
Publication statusPublished - Nov 1 2002

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics

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