COMPUTATION OF THE RELATIVE CLASS-NUMBERS OF SOME HILBERT CLASS FIELDS

Authors
LOUBOUTIN S
Citation
S. Louboutin, COMPUTATION OF THE RELATIVE CLASS-NUMBERS OF SOME HILBERT CLASS FIELDS, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 319(4), 1994, pp. 321-325
Citations number
8
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Comptes rendus de l'Academie des sciences. Serie 1, Mathematique → ACNP
ISSN journal
07644442
Volume
319
Issue
4
Year of publication
1994
Pages
321 - 325
Database
ISI
SICI code
0764-4442(1994)319:4<321:COTRCO>2.0.ZU;2-W
Abstract
We give an expression for the relative class number of any CM-field th at is suitable for numerical computation. This expression is then used in order to compute relative class numbers of 2-narrow Hilbert class fields of real quadratic fields for which their 2-Sylow subgroups of t heir ideal class groups are cyclic. These computations suggest that th ere are exactly 24 such 2-narrow Hilbert class fields with relative cl ass number one, and that they have degree 8 or 16.