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Class Numbers of Real Quadratic Function Fields of Genus One

✍ Scribed by Humio Ichimura

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 160 KB
Volume: 3
Category: Article
ISSN: 1071-5797
DOI: 10.1006/ffta.1997.0182

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✦ Synopsis

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 the class number of the integral closure of ‫ކ‬ p [X ] in K is N.

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