Class number calculation of a quartic field from the elliptic unit
Ken Nakamula (1985)
Acta Arithmetica
Similarity:
Ken Nakamula (1985)
Acta Arithmetica
Similarity:
Franz Lemmermeyer (1997)
Journal de théorie des nombres de Bordeaux
Similarity:
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.
Alan Candiotti (1974)
Compositio Mathematica
Similarity:
Daniel Shanks, Peter Weinberger (1972)
Acta Arithmetica
Similarity:
Ken Nakamula (1985)
Acta Arithmetica
Similarity:
J. E. Carroll, H. Kisilevsky (1976)
Compositio Mathematica
Similarity:
Stéphane Louboutin (1997)
Acta Arithmetica
Similarity:
Joseph E. Carroll (1975)
Compositio Mathematica
Similarity:
Ken Yamamura (1997)
Journal de théorie des nombres de Bordeaux
Similarity:
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...