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On real quadratic function fields

✍ Scribed by Erwan Le Yaouanc

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
126 KB
Volume
123
Category
Article
ISSN
0022-314X

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✦ Synopsis

Let q be a power of an odd prime number p and K := F q (T ) be the rational function field with a fixed indeterminate T . For P a prime of K, let K + P be the maximal real subfield of the P th-cyclotomic function field and O K + P its ring of integers. We prove that there exists infinitely many primes P of even degree such that the cardinal of the ideal class group Cl(O K + P ) is divisible by q. We prove also an analogous result for imaginary extensions.

📜 SIMILAR VOLUMES

Class Numbers of Real Quadratic Function
Class Numbers of Real Quadratic Function Fields of Genus One
✍ Humio Ichimura 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 160 KB

For a prime number p, let ‫ކ‬ p be the finite field of cardinality p and X ϭ X p a fixed indeterminate. We prove that for any natural number N, there exist infinitely many pairs ( p, K/‫ކ‬ p (X )) of a prime number p and a ''real'' quadratic extension K/‫ކ‬ p (X ) for which the genus of K is one and