On the Simplest Quartic Fields and Related Thue Equations

DOI10.1007/978-3-662-43799-5_7zbMath1346.11029arXiv1004.1960OpenAlexW2964186042MaRDI QIDQ2799552

Akinari Hoshi

Publication date: 12 April 2016

Published in: Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1004.1960

zbMATH Keywords

isomorphism problemfield intersection problemsimplest quartic fieldsfield isomorphism problem

Mathematics Subject Classification ID

Thue-Mahler equations (11D59) Cubic and quartic extensions (11R16) Cubic and quartic Diophantine equations (11D25) Special polynomials in general fields (12E10)

Related Items (7)

Complete solutions to a family of Thue equations of degree 12 ⋮ The Probability That Int n (D) Is Free ⋮ Merging DEL and ETL ⋮ Dynamic logics of knowledge and access ⋮ Toward a dynamic logic of questions ⋮ On the simplest sextic fields and related Thue equations ⋮ A generalization of simplest number fields and their integral basis

Uses Software

• CASA
• GAP
• Magma

Cites Work

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• On the computation of resolvents and Galois groups
• On correspondence between solutions of a family of cubic Thue equations and isomorphism classes of the simplest cubic fields
• Complete solution of the diophantine equation \(X^ 2+1=dY^ 4\) and a related family of quartic Thue equations
• Rational algebraic curves. A computer algebra approach
• Characterizing cyclic cubic extensions by automorphism polynomials
• Automorphism polynomials in cyclic cubic extensions
• The Magma algebra system. I: The user language
• Negligibility of projective linear automorphisms
• Arithmetic of Rikuna's generic cyclic polynomial and generalization of Kummer theory
• Complete solution of a family of quartic Thue equations
• Tschirnhausen transformation of a cubic generic polynomial and a \(2\)-dimensional involutive Cremona transformation
• Kummer theory for norm algebraic tori
• Elliptic curves associated with simplest quartic fields
• A parallel multi-modular algorithm for computing Lagrange resolvents
• On the field intersection problem of quartic generic polynomials via formal Tschirnhausen transformation
• Efficient computation of root numbers and class numbers of parametrized families of real abelian number fields
• On the field intersection problem of generic polynomials: a survey
• Simple families of Thue inequalities
• On simple families of cyclic polynomials
• Families of cyclic polynomials obtained from geometric generalization of Gaussian period relations
• ON THE FIELD INTERSECTION PROBLEM OF SOLVABLE QUINTIC GENERIC POLYNOMIALS
• Advanced Topics in Computional Number Theory
• Calcul de résolvantes avec les modules de Cauchy
• On the class number and unit index of simplest quartic fields
• On the practical solution of genus zero Diophantine equations
• The decomposition of primes in torsion point fields

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