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A table of quintic number fields. (English) Zbl 0822.11087

The authors present two tables: a table of all totally real fields \(F\) of degree 5 and discriminant \(\Delta_ F\) satisfying \(| \Delta_ F |< 20 000 000\) and a table of all fields \(F\) of degree 5 that are not totally real and for which \(| \Delta_ F |<5 000 000\). The Galois groups of the normal closures of these fields are also given.
The authors describe the number fields by giving irreducible polynomials \(f(T)\in\mathbb{Z} [T]\) of degree 5. It is possible to choose \(f\) to have relatively small coefficients. The authors carefully discuss their delicate estimates of the size of the coefficients of \(f(T)\). They also estimate the running time of their algorithm.
Reviewer: R.Schoof (Roma)

MSC:

11Y40 Algebraic number theory computations
11R21 Other number fields

Software:

KANT/KASH
Full Text: DOI

References:

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