A quadratic field of prime discriminant requiring three generators for its class group, and related theory
Daniel Shanks, Peter Weinberger (1972)
Acta Arithmetica
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Daniel Shanks, Peter Weinberger (1972)
Acta Arithmetica
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Pierre Kaplan, Kenneth Williams, Yoshihiko Yamamoto (1984)
Acta Arithmetica
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Michal Bulant (2002)
Acta Mathematica et Informatica Universitatis Ostraviensis
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Franz Lemmermeyer (1997)
Journal de théorie des nombres de Bordeaux
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Classical results of Rédei, Reichardt and Scholz show that unramified cyclic quartic extensions of quadratic number fields correspond to certain factorizations of its discriminant disc . In this paper we extend their results to unramified quaternion extensions of which are normal over , and show how to construct them explicitly.
Michal Bulant (1998)
Acta Mathematica et Informatica Universitatis Ostraviensis
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Ken Yamamura (1997)
Journal de théorie des nombres de Bordeaux
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We determine the structures of the Galois groups Gal of the maximal unramified extensions of imaginary quadratic number fields of conductors under the Generalized Riemann Hypothesis). For all such , is , the Hilbert class field of , the second Hilbert class field of , or the third Hilbert class field of . The use of Odlyzko’s discriminant bounds and information on the structure of class groups obtained by using the action of Galois groups on class groups is essential. We...
Alan Candiotti (1974)
Compositio Mathematica
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