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On the subfields of cyclotomic function fields

✍ Scribed by Zhao, Zhengjun; Wu, Xia

Book ID
121604436
Publisher
Springer
Year
2013
Tongue
English
Weight
110 KB
Volume
63
Category
Article
ISSN
0011-4642

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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
On the Class Numbers of the Maximal Real Subfields of Cyclotomic Function Fields, II
✍ 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

On L-functions of cyclotomic function fi
On L-functions of cyclotomic function fields
✍ Bruno AnglΓ¨s πŸ“‚ Article πŸ“… 2006 πŸ› Elsevier Science 🌐 English βš– 206 KB

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.