UPPER BOUNDS FOR THE NUMBER OF SOLUTIONS TO QUARTIC THUE EQUATIONS-Reference-Cited by-同舟云学术

UPPER BOUNDS FOR THE NUMBER OF SOLUTIONS TO QUARTIC THUE EQUATIONS

Published:2012-03 Issue:02 Volume:08 Page:335-360
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

AKHTARI SHABNAM¹

Affiliation:

1. CRM, University of Montreal, P. O. Box 6128, Centre-ville Station, Montreal, H3C 3J7, Canada

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 Theory130(1) (2010) 40–60] by giving special treatments to forms with respect to their signature.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042112500200

Reference9 articles.

1. Quartic Thue equations

2. On Thue's equation

3. Bornes effectives pour les solutions des équations enS-unités et des équations de Thue–Mahler

4. Explicit lower bounds for linear forms in two logarithms

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