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: 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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A mean value theorem for class numbers of quadratic extensions.
Contemporary Mathematics, 143:179-242, 1993. MR 1210518 (94m:11137)
- C.F. Gauss.
Yale University Press, New Haven, London, 1966. MR 0197380 (33:5545)
- D. Goldfeld and J. Hoffstein.
Eisenstein series of -integral weight and the mean value of real Dirichlet series.
Invent. Math., 80:185-208, 1985. MR 788407 (86m:11029)
- A.C. Kable and A. Yukie.
The mean value of the product of class numbers of paired quadratic fields, II.
J. Math. Soc. Japan, 55:739-764, 2003. MR 1978221 (2004g:11104a)
- D. Mumford and J. Fogarty.
Geometric invariant theory.
Springer-Verlag, Berlin, Heidelberg, New York, 2nd edition, 1982. MR 719371 (86a:14006)
- T. Shintani.
On zeta-functions associated with vector spaces of quadratic forms.
J. Fac. Sci. Univ. Tokyo, Sect IA, 22:25-66, 1975. MR 0384717 (52:5590)
- C.L. Siegel.
The average measure of quadratic forms with given discriminant and signature.
Ann. of Math., 45:667-685, 1944. MR 0012642 (7:51a)
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A mean value theorem for the square of class number times regulator of quadratic extensions.
Preprint 2004. MR 2106480 (2006c:11137)
Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, 3–8–1 Komaba Megoro-ku, Tokyo 153-0041, Japan
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.