Location of Repository

CLASS NUMBERS OF REAL CYCLOTOMIC FIELDS OF PRIME CONDUCTOR

By René Schoof

Abstract

The class numbers h + l of the real cyclotomic fields Q(ζl + ζ−1 l) are notoriously hard to compute. Indeed, the number h + l is not known for a single prime l ≥ 71. In this paper we present a table of the orders of certain subgroups of the class groups of the real cyclotomic fields Q(ζl + ζ −1 l) for the primes l<10, 000. It is quite likely that these subgroups are in fact equal to the class groups themselves, but there is at present no hope of proving this rigorously. In the last section of the paper we argue —on the basis of the Cohen-Lenstra heuristics — that the probability that our table is actually a table of class numbers h + l, is at least 98%

Year: 2002
OAI identifier: oai:CiteSeerX.psu:10.1.1.192.5362
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • http://www.ams.org/journals/mc... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.