๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

On the ideal class groups of the maximal real subfields of number fields with all roots of unity

โœ Scribed by Masato Kurihara


Publisher
European Mathematical Society
Year
1999
Tongue
English
Weight
113 KB
Volume
1
Category
Article
ISSN
1435-9855

No coin nor oath required. For personal study only.


๐Ÿ“œ SIMILAR VOLUMES


On the Class Numbers of the Maximal Real
โœ Humio Ichimura ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 275 KB

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.

On the Class Numbers of the Maximal Real
โœ Humio Ichimura ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 229 KB

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

On the Cyclotomic Unit Group and the Ide
โœ Manabu Ozaki ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 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