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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On proportional constants of the mean value of class numbers of quadratic extensions


Author: Takashi Taniguchi
Journal: Trans. Amer. Math. Soc. 359 (2007), 5517-5524
MSC (2000): Primary 11R45, 11S90
Published electronically: April 17, 2007
MathSciNet review: 2327040
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Abstract | References | Similar Articles | Additional Information

Abstract: In this article, we give a refinement of the mean value theorem for the class number of quadratic extensions obtained by Goldfeld-Hoffstein and Datskovsky. More specifically, we determine the proportional constants of the mean value for fields that satisfy any local conditions including wild ramification at places dividing $ 2$.


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Additional Information

Takashi Taniguchi
Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, 3–8–1 Komaba Megoro-ku, Tokyo 153-0041, Japan
Email: tani@ms.u-tokyo.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04221-3
PII: S 0002-9947(07)04221-3
Keywords: Density theorems, prehomogeneous vector spaces
Received by editor(s): November 15, 2004
Received by editor(s) in revised form: October 31, 2005
Published electronically: April 17, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.