Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

On the computation of class numbers of real abelian fields


Author: Tuomas Hakkarainen
Journal: Math. Comp. 78 (2009), 555-573
MSC (2000): Primary 11R29, 11Y40; Secondary 11R20, 11R27
DOI: https://doi.org/10.1090/S0025-5718-08-02169-8
Published electronically: September 4, 2008
MathSciNet review: 2448721
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: 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 $ \leq 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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 11R29, 11Y40, 11R20, 11R27

Retrieve articles in all journals with MSC (2000): 11R29, 11Y40, 11R20, 11R27


Additional Information

Tuomas Hakkarainen
Affiliation: Department of Mathematics & TUCS, Turku Centre for Computer Science, University of Turku, FI-20014 Turku, Finland

DOI: https://doi.org/10.1090/S0025-5718-08-02169-8
Keywords: Class numbers, computation, abelian fields, units
Received by editor(s): April 28, 2006
Published electronically: September 4, 2008
Additional Notes: This work was financially supported by the Turku Centre for Computer Science, TUCS
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society