Upper bounds for the number of solutions to quartic thue equations

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Abstract

We will give upper bounds for the number of integral solutions to quartic Thue equations. Our main tool here is a logarithmic curve φ(x, y) that allows us to use the theory of linear forms in logarithms. This paper improves the results of the author's earlier work with Okazaki [The quartic Thue equations, J. Number Theory 130(1) (2010) 4060] by giving special treatments to forms with respect to their signature.

Original languageEnglish (US)
Pages (from-to)335-360
Number of pages26
JournalInternational Journal of Number Theory
Volume8
Issue number2
DOIs
StatePublished - Mar 2012

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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