Power integral bases in a parametric family of totally real cyclic quintics
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Publication:4372642
DOI10.1090/S0025-5718-97-00868-5zbMath0899.11064OpenAlexW2093580033MaRDI QIDQ4372642
Publication date: 16 December 1997
Published in: Mathematics of Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0025-5718-97-00868-5
power integral basisintegral basisfamily of quintic fieldsset of fundamental unitstotally real cyclic quintic fields
Computer solution of Diophantine equations (11Y50) Algebraic number theory computations (11Y40) Multiplicative and norm form equations (11D57)
Related Items (12)
Power Integral Bases in Orders of Composite Fields ⋮ Calculating all elements of minimal index in the infinite parametric family of simplest quartic fields ⋮ The discriminant of a cyclic field of odd prime degree ⋮ Power Integral Bases in Cubic Relative Extensions ⋮ Power integral bases for real cyclotomic fields ⋮ Application of Weierstrass units to relative power integral bases ⋮ Normal integral bases for Emma Lehmer's parametric family of cyclic quintics ⋮ A parametric family of quintic Thue equations ⋮ On the order generated by the conjugates of an algebraic integer ⋮ A family of quintic cyclic fields with even class number parameterized by rational points on an elliptic curve ⋮ Finding normal integral bases of cyclic number fields of prime degree ⋮ On the indices in number fields and their computation for small degrees
Uses Software
Cites Work
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- On the resolution of index form equations in sextic fields with an imaginary quadratic subfield
- On an error term of Landau. II
- KANT V4
- Simultaneous representation of integers by a pair of ternary quadratic forms -- with an application to index form equations in quartic number fields
- Note on a Polynomial of Emma Lehmer
- Quintic Polynomials and Real Cyclotomic Fields with Large Class Number
- Computing All Power Integral Bases of Cubic Fields
- Computing all power integral bases in orders of totally real cyclic sextic number fields
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