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On the defining polynomials of maximal real cyclotomic extensions

✍ Scribed by M. Aranés; A. Arenas

Publisher
Springer Milan
Year
2008
Tongue
English
Weight
141 KB
Volume
102
Category
Article
ISSN
1578-7303

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📜 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 📂 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.

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