An inequality between class numbers and Ono's numbers associated to imaginary quadratic fields

Fumio Sairaiji; Kenichi Shimizu

doi:10.3792/pjaa.78.105

An inequality between class numbers and Ono's numbers associated to imaginary quadratic fields

Fumio Sairaiji, Kenichi Shimizu

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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 ≤ 2^pD 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 ≤ 2^pD. We also discuss lower and upper bounds for Ono's number p_D.

Original language	English
Pages (from-to)	105-108
Number of pages	4
Journal	Proceedings of the Japan Academy Series A: Mathematical Sciences
Volume	78
Issue number	7
DOIs	https://doi.org/10.3792/pjaa.78.105
Publication status	Published - 2002 Sept
Externally published	Yes

Keywords

Class number
Ono's number

ASJC Scopus subject areas

Mathematics(all)

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10.3792/pjaa.78.105

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abstract = "Ono's number pD and the class number hD, associated to an imaginary quadratic field with discriminant -D, are closely connected. For example, Frobenius-Rabinowitsch Theorem asserts that pD = 1 if and only if hD = 1. In 1986, T. Ono raised a problem whether the inequality hD ≤ 2pD 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 hD ≤ 2pD. We also discuss lower and upper bounds for Ono's number pD.",

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AB - Ono's number pD and the class number hD, associated to an imaginary quadratic field with discriminant -D, are closely connected. For example, Frobenius-Rabinowitsch Theorem asserts that pD = 1 if and only if hD = 1. In 1986, T. Ono raised a problem whether the inequality hD ≤ 2pD 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 hD ≤ 2pD. We also discuss lower and upper bounds for Ono's number pD.

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KW - Ono's number

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An inequality between class numbers and Ono's numbers associated to imaginary quadratic fields

Abstract

Keywords

ASJC Scopus subject areas

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