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...