Upper bounds for the number of solutions to quartic thue equations

Shabnam Akhtari

doi:10.1142/S1793042112500200

Upper bounds for the number of solutions to quartic thue equations

Shabnam Akhtari

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 language	English (US)
Pages (from-to)	335-360
Number of pages	26
Journal	International Journal of Number Theory
Volume	8
Issue number	2
DOIs	https://doi.org/10.1142/S1793042112500200
State	Published - Mar 2012

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1142/S1793042112500200

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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.",

author = "Shabnam Akhtari",

note = "Funding Information: I would like to thank Professor Ryotaro Okazaki for his helpful comments and suggestions. Most of this work has been done during my stays at Mathematis-ches Forschungsinstitut Oberwolfach and Max-Planck Institute for Mathematics in Bonn. I am very grateful to both institutes for support and hospitality.",

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N2 - 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.

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Upper bounds for the number of solutions to quartic thue equations

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All Science Journal Classification (ASJC) codes

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