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On L-functions of cyclotomic function fields

✍ Scribed by Bruno Anglès

Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
206 KB
Volume
116
Category
Article
ISSN
0022-314X

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✦ Synopsis

We study two criterions of cyclicity for divisor class groups of function fields, the first one involves Artin L-functions and the second one involves "affine" class groups. We show that, in general, these two criterions are not linked.

📜 SIMILAR VOLUMES

Cyclotomic Function Fields with Ideal Cl
Cyclotomic Function Fields with Ideal Class Number One
✍ Stéphan Sémirat 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 139 KB

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

On the Class Numbers of the Maximal Real
On the Class Numbers of the Maximal Real Subfields of Cyclotomic Function Fields
✍ Humio Ichimura 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 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.