|
The exponent three class group problem for some real cyclic cubic number fields
Author(s):
Stéphane
Louboutin
Journal:
Proc. Amer. Math. Soc.
130
(2002),
353-361.
MSC (1991):
Primary 11R16, 11R29, 11R42
Posted:
June 8, 2001
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We determine all the simplest cubic fields whose ideal class groups have exponent dividing  , thus generalizing the determination by G. Lettl of all the simplest cubic fields with class number  and the determination by D. Byeon of all all the simplest cubic fields with class number  . We prove that there are  simplest cubic fields with ideal class groups of exponent  (and  simplest cubic fields with ideal class groups of exponent  , i.e. with class number one).
References:
- [Ba]
- E. Bach.
Explicit bounds for primality testing and related problems.
Math. Comp. 55 (1990), 355-380. MR 91m:11096 - [BS]
- E. Bach and J. Sorenson.
Explicit bounds for primes in residue classes.
Math. Comp. 65 (1996), 1717-1735. MR 97a:11143 - [BW]
- J. Buchmann, J. and H. C. Williams.
On the computation of the class number of an algebraic number field.
Math. Comp. 53 (1989), 679-688. MR 90a:11128 - [Bye]
- D. Byeon.
Class number  problem for the simplest cubic fields.
Proc. Amer. Math. Soc. 128 (2000), 1319-1323. MR 2000j:11158 - [Cus]
- T. W. Cusick.
Lower bounds for regulators.
Lectures Notes in Math. 1068 (1984), 63-73. MR 85k:11052 - [Let]
- G. Lettl.
A lower bound for the class number of certain cubic number fields.
Math. Comp. 46 (1986), 659-666. MR 87e:11123 - [Lou1]
- S. Louboutin.
Lower bounds for relative class numbers of CM-fields.
Proc. Amer. Math. Soc. 120 (1994), 425-434. MR 94d:11089 - [Lou2]
- S. Louboutin.
Calcul du nombre de classes des corps de nombres.
Pacific J. Math. 171 (1995), 455-467. MR 97a:11176 - [Lou3]
- S. Louboutin.
Class number problems for cubic number fields.
Nagoya Math. J. 138 (1995), 199-208. MR 96f:11145 - [Lou4]
- S. Louboutin.
Class-group problems for cubic number fields.
Japan. J. Math. 23 (1997), 365-378. MR 99a:11124 - [Lou5]
- S. Louboutin.
Computation of relative class numbers of imaginary abelian number fields.
Experimental Math. 7 (1998), 293-303. MR 2000c:11207 - [Lou6]
- S. Louboutin.
Class number and class group problems for some non-normal totally real cubic number fields.
In preparation. - [LP]
- F. Lemmermeyer and A. Pethö.
Simplest cubic fields.
Manuscripta Math. 88 (1995), 53-58. MR 96g:11131 - [Ric]
- C. Ricci.
Ricerche arithmetiche sui polinomi.
Rend. Circ. Mat. Palermo 57 (1933), 433-475. - [Sh]
- D. Shanks.
The simplest cubic fields.
Math. Comp. 28 (1974), 1137-1152. MR 50:4537 - [Wa]
- L. C. Washington.
Class numbers of the simplest cubic fields.
Math. Comp. 48 (1987), 371-384. MR 88a:11107
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(1991):
11R16, 11R29, 11R42
Retrieve articles in all Journals with MSC
(1991):
11R16, 11R29, 11R42
Additional Information:
Stéphane
Louboutin
Affiliation:
Institut de Mathématiques de Luminy, UPR 906, 163, avenue de Luminy, Case 907, 13288 Marseille Cedex 9, France
Email:
loubouti@iml.univ-mrs.fr
DOI:
10.1090/S0002-9939-01-06168-8
PII:
S 0002-9939(01)06168-8
Keywords:
Simplest cubic field,
cubic field,
class number,
class group
Received by editor(s):
June 26, 2000
Posted:
June 8, 2001
Communicated by:
David E. Rohrlich
Copyright of article:
Copyright
2001,
American Mathematical Society
Forward Citation(s): Information for authors on submitting citations The following works have cited this article Louboutin S., Class number and class group problems for some non-normal totally real cubic number fields, Manuscripta Math. 106 (2001), 411-427. (english) MR 2002j:11123
|
Comments: webmaster@ams.org