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The class number of cyclotomic function fields

✍ Scribed by Steven Galovich; Michael Rosen

Publisher
Elsevier Science
Year
1981
Tongue
English
Weight
619 KB
Volume
13
Category
Article
ISSN
0022-314X

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πŸ“œ SIMILAR VOLUMES

On the Class Numbers of the Maximal Real
On the Class Numbers of the Maximal Real Subfields of Cyclotomic Function Fields
✍ Humio Ichimura πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 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
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✍ Humio Ichimura πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 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

Cyclotomic Function Fields with Ideal Cl
Cyclotomic Function Fields with Ideal Class Number One
✍ StΓ©phan SΓ©mirat πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 139 KB

We list all imaginary cyclotomic extensions ‫ކ‬ x, ⌳ r‫ކ‬ x with ideal class q M Ε½ x . q number equal to one. Apart from the zero genus ones, there are 17 solutions up to Ε½ . ‫ކ‬ x -isomorphism: 13 of them are defined over ‫ކ‬ and the 4 remainings are q 3 defined over ‫ކ‬ .

Class numbers of cyclotomic fields
Class numbers of cyclotomic fields
✍ Gary Cornell; Lawrence C Washington πŸ“‚ Article πŸ“… 1985 πŸ› Elsevier Science 🌐 English βš– 813 KB