Unramified quaternion extensions of quadratic number fields

Franz Lemmermeyer

Journal de théorie des nombres de Bordeaux (1997)

  • Volume: 9, Issue: 1, page 51-68
  • ISSN: 1246-7405

Abstract

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Classical results of Rédei, Reichardt and Scholz show that unramified cyclic quartic extensions of quadratic number fields k correspond to certain factorizations of its discriminant disc k . In this paper we extend their results to unramified quaternion extensions of k which are normal over ℚ , and show how to construct them explicitly.

How to cite

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Lemmermeyer, Franz. "Unramified quaternion extensions of quadratic number fields." Journal de théorie des nombres de Bordeaux 9.1 (1997): 51-68. <http://eudml.org/doc/248015>.

@article{Lemmermeyer1997,
abstract = {Classical results of Rédei, Reichardt and Scholz show that unramified cyclic quartic extensions of quadratic number fields $k$ correspond to certain factorizations of its discriminant disc $k$. In this paper we extend their results to unramified quaternion extensions of $k$ which are normal over $\mathbb \{Q\}$, and show how to construct them explicitly.},
author = {Lemmermeyer, Franz},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {unramified quaternion extensions; number fields; unramified dihedral extensions of quadratic number fields},
language = {eng},
number = {1},
pages = {51-68},
publisher = {Université Bordeaux I},
title = {Unramified quaternion extensions of quadratic number fields},
url = {http://eudml.org/doc/248015},
volume = {9},
year = {1997},
}

TY - JOUR
AU - Lemmermeyer, Franz
TI - Unramified quaternion extensions of quadratic number fields
JO - Journal de théorie des nombres de Bordeaux
PY - 1997
PB - Université Bordeaux I
VL - 9
IS - 1
SP - 51
EP - 68
AB - Classical results of Rédei, Reichardt and Scholz show that unramified cyclic quartic extensions of quadratic number fields $k$ correspond to certain factorizations of its discriminant disc $k$. In this paper we extend their results to unramified quaternion extensions of $k$ which are normal over $\mathbb {Q}$, and show how to construct them explicitly.
LA - eng
KW - unramified quaternion extensions; number fields; unramified dihedral extensions of quadratic number fields
UR - http://eudml.org/doc/248015
ER -

References

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