Computing all power integral bases in orders of totally real cyclic sextic number fields

DOI10.1090/S0025-5718-96-00708-9zbMath0857.11069OpenAlexW1965772345MaRDI QIDQ4878582

István Gaál

Publication date: 17 March 1997

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-96-00708-9

zbMATH Keywords

algorithmpower integral basesindex forminhomogeneous Thue equationrelative norm equationcyclic sextic fields of smallest discriminantsorders of totally real cyclic sextic number fields

Mathematics Subject Classification ID

Computer solution of Diophantine equations (11Y50) Algebraic number theory computations (11Y40) Multiplicative and norm form equations (11D57) Totally real fields (11R80)

Related Items (20)

Unnamed Item ⋮ Integral bases and monogenity of the simplest sextic fields ⋮ Power Integral Bases in Cubic Relative Extensions ⋮ Power integral bases in a parametric family of totally real cyclic quintics ⋮ Calculating power integral bases by using relative power integral bases ⋮ A hybrid Gröbner bases approach to computing power integral bases ⋮ Power integral bases for real cyclotomic fields ⋮ Computing power integral bases in quartic relative extensions ⋮ On the resolution of relative Thue equations ⋮ Application of Weierstrass units to relative power integral bases ⋮ Power bases for 2-power cyclotomic fields ⋮ Monogenesis of the rings of integers in certain imaginary abelian fields ⋮ MONOGENEITY IN CYCLOTOMIC FIELDS ⋮ Power bases for cyclotomic integer rings ⋮ On the solution of units and index form equations in algebraic number fields ⋮ Calculating ``small solutions of inhomogeneous relative Thue inequalities ⋮ Solving index form equations in fields of degree 9 with cubic subfields ⋮ Calculating “Small” Solutions of Relative Thue Equations ⋮ On a problem of Hasse for certain imaginary Abelian fields ⋮ On the resolution of resultant type equations

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