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On the class numbers of cyclotomic fields

✍ Scribed by Larry Joel Goldstein

Publisher
Elsevier Science
Year
1973
Tongue
English
Weight
223 KB
Volume
5
Category
Article
ISSN
0022-314X

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πŸ“œ SIMILAR VOLUMES

On the Class Numbers of the Maximal Real
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For a prime number l, let h> J be the class number of the maximal real subfield of the l-th cyclotomic field. For each natural number N, it is plausible but not yet proved that there exist infinitely many prime numbers l with h> J 'N. We prove an analogous assertion for cyclotomic function fields.

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Let q be a power of a prime number p and k=F q (T ) the rational function field with a fixed indeterminate T. For an irreducible monic P=P(T ) in R=F q [T], let k(P) + be the maximal real subfield of the P th cyclotomic function field and h + T (P) the class number of k(P) + associated to R. We prov

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✍ Manabu Ozaki πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 1001 KB

Let K be a real abelian number field satisfying certain conditions and K n the n th layer of the cyclotomic Z p -extension of K. We study the relation between the p-Sylow subgroup of the ideal class group and that of the unit group module the cyclotomic unit group of K n . We give certain sufficient