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Mean value of L-functions and the number of classes of a cyclotomic field

โœ Scribed by I. Sh. Slavutskii

Publisher
Springer US
Year
1988
Tongue
English
Weight
352 KB
Volume
43
Category
Article
ISSN
1573-8795

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๐Ÿ“œ SIMILAR VOLUMES

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