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Cohen, Henri; Roblot, Xavier-François

Computing the Hilbert class field of real quadratic fields. (English) Zbl 1042.11075

Math. Comput. 69, No. 231, 1229-1244 (2000).
Summary: Using the units appearing in Stark’s conjectures on the values of \(L\)-functions at \(s=0\), we give a complete algorithm for computing an explicit generator of the Hilbert class field of a real quadratic field.

Cited in 6 Documents

MSC:

11Y40 Algebraic number theory computations
11R37 Class field theory
11R42 Zeta functions and \(L\)-functions of number fields
11Y35 Analytic computations

Software:

PARI/GP
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\textit{H. Cohen} and \textit{X.-F. Roblot}, Math. Comput. 69, No. 231, 1229--1244 (2000; Zbl 1042.11075)
Full Text: DOI

Online Encyclopedia of Integer Sequences:

Discriminants of real quadratic fields with unique factorization.
Discriminants of real quadratic number fields with class number 2 such that Hilbert class field has splitting field Q(sqrt(5)).
Discriminants of real quadratic number fields with class number 2 such that Hilbert class field has splitting field Q(sqrt(2)).
Fundamental discriminants of real quadratic number fields with odd class number > 1.
Fundamental discriminants of real quadratic number fields with odd class number > 1 whose fundamental unit has norm 1.
Fundamental discriminants of real quadratic number fields with odd class number > 1 whose fundamental unit has norm -1.

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