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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On real quadratic function fields of Chowla type with ideal class number one
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by Keqin Feng and Weiqun Hu PDF
Proc. Amer. Math. Soc. 127 (1999), 1301-1307 Request permission

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