Exceptional units in a family of quartic number fields

DOI10.1090/S0025-5718-98-00958-2zbMath0920.11074OpenAlexW2028831586MaRDI QIDQ4383192

Gerhard Niklasch, Nigel P. Smart

Publication date: 24 March 1998

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-98-00958-2

zbMATH Keywords

Baker's methodlinear forms in two logarithmsexceptional unitsunit equationquartic number fieldsAnkeny-Brauer-Chowla number fields

Mathematics Subject Classification ID

Units and factorization (11R27) Cubic and quartic extensions (11R16) Exponential Diophantine equations (11D61) Linear forms in logarithms; Baker's method (11J86)

Related Items (7)

On the sums of squares of exceptional units in residue class rings ⋮ Integral Points on Elliptic Curves Defined by Simplest Cubic Fields ⋮ On the sumsets of exceptional units in \(\mathbb {Z}_n\) ⋮ On a question of \(f\)-exunits in \(\mathbb{Z}/n\mathbb{Z} \) ⋮ On sums of polynomial-type exceptional units in \(\mathbb{Z}/n\mathbb{Z}\) ⋮ Sums of exceptional units in residue class rings ⋮ Units in some families of algebraic number fields

Cites Work

• Verification of a conjecture of E. Thomas
• Complete solutions to a family of cubic Diophantine equations
• On the practical solution of the Thue equation
• Euclidean number fields of large degree
• Linear forms in two logarithms and interpolation determinants
• Sur un type particulier d'unités algébriques
• Solving discriminant form equations via unit equations
• Complete Solutions to Families of Quartic Thue Equations
• The Solution of Triangularly Connected Decomposable Form Equations
• Complete solutions of a family of quartic Thue and index form equations
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