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On class numbers of quadratic extensions¶over function fields

✍ Scribed by Iwao Kimura

Publisher
Springer
Year
1998
Tongue
English
Weight
132 KB
Volume
97
Category
Article
ISSN
0025-2611

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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

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The analogues of the classical Kronecker and Hurwitz class number relations for function fields of any positive characteristic are obtained by a method parallel to the classical proof. In the case of even characteristic, purely inseparable orders also have to be taken into account. A subtle point is