On the computation of class numbers of real abelian fields

Hakkarainen, Tuomas

doi:10.1090/S0025-5718-08-02169-8

On the computation of class numbers of real abelian fields
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Math. Comp. 78 (2009), 555-573 Request permission

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.

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