On the computation of class numbers of real abelian fields
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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
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Additional Information
- Tuomas Hakkarainen
- Affiliation: Department of Mathematics & TUCS, Turku Centre for Computer Science, University of Turku, FI-20014 Turku, Finland
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2448721