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Fiber products and class groups of hyperelliptic curves


Author: Jeffrey D. Achter
Journal: Proc. Amer. Math. Soc. 138 (2010), 3159-3161
MSC (2010): Primary 11R58; Secondary 11R29, 14H05
DOI: https://doi.org/10.1090/S0002-9939-10-10461-4
Published electronically: April 21, 2010
MathSciNet review: 2653940
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \mathbb{F}_q$ be a finite field of odd characteristic, and let $ N$ be an odd natural number. An explicit fiber product construction shows that if $ N$ divides the class number of some quadratic function field over $ \mathbb{F}_q$, then it does so for infinitely many such function fields.


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Additional Information

Jeffrey D. Achter
Affiliation: Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523
Email: j.achter@colostate.edu

DOI: https://doi.org/10.1090/S0002-9939-10-10461-4
Received by editor(s): December 18, 2009
Published electronically: April 21, 2010
Additional Notes: The author was partially supported by NSA grant H98230-08-1-0051.
Communicated by: Ken Ono
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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