On correspondence between solutions of a family of cubic Thue equations and isomorphism classes of the simplest cubic fields

DOI10.1016/j.jnt.2011.05.001zbMath1258.11054arXiv0810.3374OpenAlexW1999025975MaRDI QIDQ640028

Akinari Hoshi

Publication date: 12 October 2011

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0810.3374

zbMATH Keywords

field isomorphism problemssimplest cubic Thue equation

Mathematics Subject Classification ID

Thue-Mahler equations (11D59) Cubic and quartic extensions (11R16) Cubic and quartic Diophantine equations (11D25)

Related Items (7)

Complete solutions to a family of Thue equations of degree 12 ⋮ The characterization of cyclic cubic fields with power integral bases ⋮ On the simplest sextic fields and related Thue equations ⋮ On the Simplest Quartic Fields and Related Thue Equations ⋮ A generalization of simplest number fields and their integral basis ⋮ Non-Galois cubic number fields with exceptional units. II ⋮ On cubic Thue equations and the indices of algebraic integers in cubic fields

Uses Software

• Magma

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the resolution of Thue inequalities
• Verification of a conjecture of E. Thomas
• Complete solutions to a family of cubic Diophantine equations
• On cubic Galois field extensions
• Solving Thue equations of high degree
• Characterizing cyclic cubic extensions by automorphism polynomials
• Automorphism polynomials in cyclic cubic extensions
• The Magma algebra system. I: The user language
• Arithmetic of Rikuna's generic cyclic polynomial and generalization of Kummer theory
• Linear forms in two logarithms and interpolation determinants
• Simplest cubic fields
• Cyclic cubic field with explicit Artin symbols
• Number of solutions for cubic Thue equations with automorphisms
• A geometric framework for the subfield problem of generic polynomials via Tschirnhausen transformation
• On the field intersection problem of quartic generic polynomials via formal Tschirnhausen transformation
• Cubic Thue Equations
• On the field intersection problem of generic polynomials: a survey
• Class Numbers of the Simplest Cubic Fields
• The Simplest Cubic Fields
• Simple families of Thue inequalities
• On the family of Thue equations x³ - (n-1)x²y - (n+2)xy² - y³ = k
• ON THE FIELD INTERSECTION PROBLEM OF SOLVABLE QUINTIC GENERIC POLYNOMIALS
• On the family of Thue equation|x 3+mx2y−(m+3)xy2+y3|=k
• The decomposition of primes in torsion point fields

This page was built for publication: On correspondence between solutions of a family of cubic Thue equations and isomorphism classes of the simplest cubic fields