Functiones et Approximatio Commentarii Mathematici

On the simplest sextic fields and related Thue equations

Akinari Hoshi

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Abstract

We consider the parametric family of sextic Thue equations $$x^6-2mx^5y-5(m+3)x^4y^2-20x^3y^3+5mx^2y^4+2(m+3)xy^5+y^6=\lambda$$ where $m\in\mathbb{Z}$ is an integer and $\lambda$ is a divisor of $27(m^2+3m+9)$. We show that the only solutions to the equations are the trivial ones with $xy(x+y)(x-y)(x+2y)(2x+y)=0$.

Article information

Source
Funct. Approx. Comment. Math., Volume 47, Number 1 (2012), 35-49.

Dates
First available in Project Euclid: 25 September 2012

Permanent link to this document
https://projecteuclid.org/euclid.facm/1348578275

Digital Object Identifier
doi:10.7169/facm/2012.47.1.3

Mathematical Reviews number (MathSciNet)
MR2987109

Zentralblatt MATH identifier
1320.11029

Subjects
Primary: 11D41: Higher degree equations; Fermat's equation
Secondary: 11D59: Thue-Mahler equations 11R20: Other abelian and metabelian extensions 11Y40: Algebraic number theory computations 12F10: Separable extensions, Galois theory

Keywords
sextic Thue equations simplest sextic fields field isomorphism problem multi-resolvent polynomial

Citation

Hoshi, Akinari. On the simplest sextic fields and related Thue equations. Funct. Approx. Comment. Math. 47 (2012), no. 1, 35--49. doi:10.7169/facm/2012.47.1.3. https://projecteuclid.org/euclid.facm/1348578275


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