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 .

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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:
https://doi.org/10.1090/S0002-9947-07-04221-3

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.