The imaginary abelian number fields with class numbers equal to their genus class numbers

Ku-Young Chang; Soun-Hi Kwon

Journal de théorie des nombres de Bordeaux (2000)

  • Volume: 12, Issue: 2, page 349-365
  • ISSN: 1246-7405

Abstract

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We know that there exist only finitely many imaginary abelian number fields with class numbers equal to their genus class numbers. Such non-quadratic cyclic number fields are completely determined in [Lou2,4] and [CK]. In this paper we determine all non-cyclic abelian number fields with class numbers equal to their genus class numbers, thus the one class in each genus problem is solved, except for the imaginary quadratic number fields.

How to cite

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Chang, Ku-Young, and Kwon, Soun-Hi. "The imaginary abelian number fields with class numbers equal to their genus class numbers." Journal de théorie des nombres de Bordeaux 12.2 (2000): 349-365. <http://eudml.org/doc/248484>.

@article{Chang2000,
abstract = {We know that there exist only finitely many imaginary abelian number fields with class numbers equal to their genus class numbers. Such non-quadratic cyclic number fields are completely determined in [Lou2,4] and [CK]. In this paper we determine all non-cyclic abelian number fields with class numbers equal to their genus class numbers, thus the one class in each genus problem is solved, except for the imaginary quadratic number fields.},
author = {Chang, Ku-Young, Kwon, Soun-Hi},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {genus class number; CM fields; abelian fields},
language = {eng},
number = {2},
pages = {349-365},
publisher = {Université Bordeaux I},
title = {The imaginary abelian number fields with class numbers equal to their genus class numbers},
url = {http://eudml.org/doc/248484},
volume = {12},
year = {2000},
}

TY - JOUR
AU - Chang, Ku-Young
AU - Kwon, Soun-Hi
TI - The imaginary abelian number fields with class numbers equal to their genus class numbers
JO - Journal de théorie des nombres de Bordeaux
PY - 2000
PB - Université Bordeaux I
VL - 12
IS - 2
SP - 349
EP - 365
AB - We know that there exist only finitely many imaginary abelian number fields with class numbers equal to their genus class numbers. Such non-quadratic cyclic number fields are completely determined in [Lou2,4] and [CK]. In this paper we determine all non-cyclic abelian number fields with class numbers equal to their genus class numbers, thus the one class in each genus problem is solved, except for the imaginary quadratic number fields.
LA - eng
KW - genus class number; CM fields; abelian fields
UR - http://eudml.org/doc/248484
ER -

References

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