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Sept. 2002 An inequality between class numbers and Ono's numbers associated to imaginary quadratic fields
Fumio Sairaiji, Kenichi Shimizu
Proc. Japan Acad. Ser. A Math. Sci. 78(7): 105-108 (Sept. 2002). DOI: 10.3792/pjaa.78.105

Abstract

Ono's number $p_D$ and the class number $h_D$, associated to an imaginary quadratic field with discriminant $-D$, are closely connected. For example, Frobenius-Rabinowitsch Theorem asserts that $p_D = 1$ if and only if $h_D = 1$. In 1986, T. Ono raised a problem whether the inequality $h_D \leq 2^{p_D}$ holds. However, in our previous paper [8], we saw that there are infinitely many $D$ such that the inequality does not hold. In this paper we give a modification to the inequality $h_D \leq 2^{p_D}$. We also discuss lower and upper bounds for Ono's number $p_D$.

Citation

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Fumio Sairaiji. Kenichi Shimizu. "An inequality between class numbers and Ono's numbers associated to imaginary quadratic fields." Proc. Japan Acad. Ser. A Math. Sci. 78 (7) 105 - 108, Sept. 2002. https://doi.org/10.3792/pjaa.78.105

Information

Published: Sept. 2002
First available in Project Euclid: 23 May 2006

zbMATH: 1052.11070
MathSciNet: MR1930211
Digital Object Identifier: 10.3792/pjaa.78.105

Subjects:
Primary: 11R11
Secondary: 11R29

Keywords: Class number , Ono's number

Rights: Copyright © 2002 The Japan Academy

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Vol.78 • No. 7 • Sept. 2002
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