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On the Computation of Class Numbers of Real Abelian Fields

Tuomas Hakkarainen, On the Computation of Class Numbers of Real Abelian Fields. TUCS Technical Reports 770, Turku Centre for Computer Science, 2006.

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 <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.

Files:

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BibTeX entry:

@TECHREPORT{tHakkarainen06a,
  title = {On the Computation of Class Numbers of Real Abelian Fields},
  author = {Hakkarainen, Tuomas},
  number = {770},
  series = {TUCS Technical Reports},
  publisher = {Turku Centre for Computer Science},
  year = {2006},
  keywords = {Class numbers, computation, abelian fields, units},
  ISBN = {952-12-1731-6},
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

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