Name
Abstract | ||
|---|---|---|
The class numbers hl+ of the real cyclotomic fields Q(ζl + + ζl+-1) are notoriously hard to compute. Indeed, the number hl+ 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 + ζl-1) 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 hl+, is at least 98%. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1090/S0025-5718-02-01432-1 | Math. Comput. |
Keywords | Field | DocType |
real cyclotomic field,number hl,single prime l,cohen-lenstra heuristics-that,last section,prime conductor,class group,certain subgroup,class numbers hl,primes l | Prime (order theory),Cyclotomic field,Abelian group,Quotient group,Combinatorics,Mathematical analysis,Group theory,Pure mathematics,Finite group,Cohomology,Number theory,Mathematics | Journal |
Volume | Issue | ISSN |
72 | 242 | 0025-5718 |
Citations | PageRank | References |
6 | 1.48 | 2 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| René Schoof | 1 | 112 | 32.70 |