HT90 and ``simplest number fields

zbMath1300.12004arXiv1207.6099MaRDI QIDQ358946

Kurt Foster

Publication date: 9 August 2013

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.6099

zbMATH Keywords

Hilbert's Theorem 90

Mathematics Subject Classification ID

Separable extensions, Galois theory (12F10) Quadratic extensions (11R11) Inverse Galois theory (12F12) Polynomials (irreducibility, etc.) (11R09) Special polynomials in general fields (12E10)

Related Items (6)

Invariant rational functions, linear fractional transformations and irreducible polynomials over finite fields ⋮ Cubic Polynomials, Linear Shifts, and Ramanujan Simple Cubics ⋮ Trace and norm of indecomposable integers in cubic orders ⋮ Solving discrete logarithms on a 170-bit MNT curve by pairing reduction ⋮ A generalization of simplest number fields and their integral basis ⋮ A short-list of pairing-friendly curves resistant to special TNFS at the 128-bit security level

Cites Work

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• Normal integral bases for Emma Lehmer's parametric family of cyclic quintics
• Euclidean fields having a large Lenstra constant
• An inequality relating the regulator and the discriminant of a number field
• A characterization of C-fields via Galois groups
• Unités d'une famille de corps cycliques réels de degré 6 liés à la courbe modulaire \(X_ 1(13)\). (Units of a family of real cyclic fields of degree 6 related to the modular curve \(X_ 1(13))\)
• Euclidean number fields of large degree
• Characterizing cyclic cubic extensions by automorphism polynomials
• Automorphism polynomials in cyclic cubic extensions
• Class numbers of cubic cyclic fields
• On a parameterized family of quadratic and cubic fields
• Sur un type particulier d'unités algébriques
• A ratio ergodic theorem for Borel actions of ℤ^d×ℝ^k
• A Device for Generating Fields of Even Class Number
• Note on a Polynomial of Emma Lehmer
• Efficient computation of root numbers and class numbers of parametrized families of real abelian number fields
• Class Numbers of the Simplest Cubic Fields
• Quintic Polynomials and Real Cyclotomic Fields with Large Class Number
• Connection Between Gaussian Periods and Cyclic Units
• Unit Groups and Class Numbers of Real Cyclic Octic Fields
• A Family of Cyclic Quartic Fields Arising from Modular Curves
• The Simplest Cubic Fields
• Simple families of Thue inequalities
• Arithmetic properties of periodic points of quadratic maps, II
• Tables of octic fields with a quartic subfield
• On simple families of cyclic polynomials
• Special Units in Real Cyclic Sextic Fields
• On the class number and unit index of simplest quartic fields

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