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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On real quadratic function fields
of Chowla type with ideal class number one


Authors: Keqin Feng and Weiqun Hu
Journal: Proc. Amer. Math. Soc. 127 (1999), 1301-1307
MSC (1991): Primary 11R11, 11R29
Published electronically: January 27, 1999
MathSciNet review: 1622805
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $\mathbb{F}_q$ be the finite field with $q$ elements, (2${\not|}q$), $k= \mathbb{F}_q(x)$, $K=k(\sqrt{D})$ where $D=D(x) =A(x)^2+a$ is a square-free polynomial in $\mathbb{F}_q[x]$ with $\deg A(x)\geq 1$ and $a\in \mathbb{ F}_q^*$. In this paper several equivalent conditions for the ideal class number $h(O_K)$ to be one are presented and all such quadratic function fields with $h(O_K)=1$ are determined.


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Additional Information

Keqin Feng
Affiliation: Graduate School at Beijing, University of Science and Technology of China, P. O. Box 3908, Beijing 100039, People’s Republic of China

Weiqun Hu
Affiliation: The Fundamental Science Department, Nanjing Agriculture College, Nanjing 210038, People’s Republic of China

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05004-2
PII: S 0002-9939(99)05004-2
Keywords: Quadradic field, function field, class number
Received by editor(s): August 20, 1997
Published electronically: January 27, 1999
Additional Notes: Research supported by the Natural Science Foundation and the National Educational Committee of China.
Communicated by: David E. Rohrlich
Article copyright: © Copyright 1999 American Mathematical Society