On real quadratic function fields of Chowla type with ideal class number one
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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.References
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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
- 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
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 1301-1307
- MSC (1991): Primary 11R11, 11R29
- DOI: https://doi.org/10.1090/S0002-9939-99-05004-2
- MathSciNet review: 1622805