On the existence of Minkowski units in totally real cyclic fields

František Marko[1]

  • [1] Pennsylvania State University 76 University Drive Hazleton, PA 18202, USA and Mathematical Institute Slovak Academy of Sciences Štefánikova 49 814 38 Bratislava, Slovakia

Journal de Théorie des Nombres de Bordeaux (2005)

  • Volume: 17, Issue: 1, page 195-206
  • ISSN: 1246-7405

Abstract

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Let K be a totally real cyclic number field of degree n that is the product of two distinct primes and such that the class number of the n -th cyclotomic field equals 1. We derive certain necessary and sufficient conditions for the existence of a Minkowski unit for K .

How to cite

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Marko, František. "On the existence of Minkowski units in totally real cyclic fields." Journal de Théorie des Nombres de Bordeaux 17.1 (2005): 195-206. <http://eudml.org/doc/249434>.

@article{Marko2005,
abstract = {Let $K$ be a totally real cyclic number field of degree $n$ that is the product of two distinct primes and such that the class number of the $n$-th cyclotomic field equals 1. We derive certain necessary and sufficient conditions for the existence of a Minkowski unit for $K$.},
affiliation = {Pennsylvania State University 76 University Drive Hazleton, PA 18202, USA and Mathematical Institute Slovak Academy of Sciences Štefánikova 49 814 38 Bratislava, Slovakia},
author = {Marko, František},
journal = {Journal de Théorie des Nombres de Bordeaux},
language = {eng},
number = {1},
pages = {195-206},
publisher = {Université Bordeaux 1},
title = {On the existence of Minkowski units in totally real cyclic fields},
url = {http://eudml.org/doc/249434},
volume = {17},
year = {2005},
}

TY - JOUR
AU - Marko, František
TI - On the existence of Minkowski units in totally real cyclic fields
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2005
PB - Université Bordeaux 1
VL - 17
IS - 1
SP - 195
EP - 206
AB - Let $K$ be a totally real cyclic number field of degree $n$ that is the product of two distinct primes and such that the class number of the $n$-th cyclotomic field equals 1. We derive certain necessary and sufficient conditions for the existence of a Minkowski unit for $K$.
LA - eng
UR - http://eudml.org/doc/249434
ER -

References

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  1. L. Bouvier, J. PayanModules sur certains anneaux de Dedekind. J. Reine Angew. Math. 274/275 (1975), 278–286. Zbl0309.12006MR374084
  2. R. KučeraOn bases of the Stickelberger ideal and of the group of circular units of a cyclotomic field. J. Number Theory 40 (1992), 284–316. Zbl0744.11052MR1154041
  3. F. MarkoOn the existence of p -units and Minkowski units in totally real cyclic fields. Abh. Math. Sem. Univ. Hamburg 66 (1996), 89–111. Zbl0869.11087MR1418221
  4. N. MoserUnités et nombre de classes d’une extension Galoisienne diédrale de ℚ . Abh. Math. Sem. Univ. Hamburg 48 (1979), 54–75. Zbl0387.12005MR537446

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