ON THE COMPUTATION OF CLASS NUMBERS OF REAL ABELIAN FIELDS

被引：4

作者：

Hakkarainen, Tuomas ^{[1
]}

机构：

[1] Univ Turku, Dept Math & Tucs, Turku Ctr Comp Sci, FI-20014 Turku, Finland

来源：

MATHEMATICS OF COMPUTATION | 2009年 / 78卷 / 265期

关键词：

Class numbers; computation; abelian fields; units; CYCLOTOMIC FIELDS; EXTENSIONS; HEURISTICS; UNITS;

D O I：

10.1090/S0025-5718-08-02169-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we give a procedure to search for prime divisors of class numbers of real abelian fields and present a table of odd primes < 10000 not dividing the degree that divide the class numbers of fields of conductor <= 2000. Cohen-Lenstra heuristics allow us to conjecture that no larger prime divisors should exist. Previous computations have been largely limited to prime power conductors.

引用

页码：555 / 573

页数：19

共 50 条

[1] Efficient computation of class numbers of real abelian number fields
Louboutin, SR
ALGORITHMIC NUMBER THEORY, 2002, 2369 : 134 - 147
[2] Efficient computation of root numbers and class numbers of parametrized families of real abelian number fields
Louboutin, Stephane R.
MATHEMATICS OF COMPUTATION, 2006, 76 (257) : 455 - 473
[3] Computation of relative class numbers of imaginary abelian number fields
Louboutin, S
EXPERIMENTAL MATHEMATICS, 1998, 7 (04) : 293 - 303
[4] CLASS-NUMBERS OF CERTAIN REAL ABELIAN-FIELDS
KIM, JM
ACTA ARITHMETICA, 1995, 72 (04) : 335 - 345
[5] COMPUTATION OF INDEPENDENT UNITS AND CLASS NUMBERS IN TOTALLY REAL QUARTIC FIELDS
POHST, M
COMPUTING, 1975, 14 (1-2) : 67 - 78
[6] On class numbers of division fields of abelian varieties
Garnek, Jedrzej
JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX, 2019, 31 (01): : 227 - 242
[7] Class numbers of imaginary abelian number fields
Chang, KY
Kwon, SH
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 128 (09) : 2517 - 2528
[8] Class number of real Abelian fields
Jakubec, S.
Pasteka, M.
Schinzel, A.
JOURNAL OF NUMBER THEORY, 2015, 148 : 365 - 371
[9] Class formulae for real abelian fields
Belliard, JR
Do, TNQ
ANNALES DE L INSTITUT FOURIER, 2001, 51 (04) : 903 - 937
[10] Computation of the p-part of the ideal class group of certain real abelian fields
Sumida-Takahashi, Hiroki
MATHEMATICS OF COMPUTATION, 2007, 76 (258) : 1059 - 1071

← 1 2 3 4 5 →