Inequalities of Ono numbers and class numbers associated to imaginary quadratic fields

Kenichi Shimizu

doi:10.3792/pjaa.85.46

Inequalities of Ono numbers and class numbers associated to imaginary quadratic fields

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

Abstract

We denote by h_D the class number and by pD the Ono number of the imaginary quadratic fields Q(√-D). Sairaiji-Shimizu [2] showed that there are infinitely many imaginary quadratic fields such that the inequality h_D > c^pD holds for any real number. On the other hand we have the possibility that h_D 5 c^pD holds for infinitely many imaginary quadratic fields for the same real number c. In this paper, given a real number c, we consider whether h_D 5 c^pD holds for infinitely many imaginary quadratic fields or not.

Original language	English
Pages (from-to)	46-48
Number of pages	3
Journal	Proceedings of the Japan Academy Series A: Mathematical Sciences
Volume	85
Issue number	4
DOIs	https://doi.org/10.3792/pjaa.85.46
Publication status	Published - 2009 Apr
Externally published	Yes

Keywords

Class number
Ono number

ASJC Scopus subject areas

Mathematics(all)

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10.3792/pjaa.85.46

Cite this

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abstract = "We denote by hD the class number and by pD the Ono number of the imaginary quadratic fields Q(√-D). Sairaiji-Shimizu [2] showed that there are infinitely many imaginary quadratic fields such that the inequality hD > cpD holds for any real number. On the other hand we have the possibility that hD 5 cpD holds for infinitely many imaginary quadratic fields for the same real number c. In this paper, given a real number c, we consider whether hD 5 cpD holds for infinitely many imaginary quadratic fields or not.",

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AB - We denote by hD the class number and by pD the Ono number of the imaginary quadratic fields Q(√-D). Sairaiji-Shimizu [2] showed that there are infinitely many imaginary quadratic fields such that the inequality hD > cpD holds for any real number. On the other hand we have the possibility that hD 5 cpD holds for infinitely many imaginary quadratic fields for the same real number c. In this paper, given a real number c, we consider whether hD 5 cpD holds for infinitely many imaginary quadratic fields or not.

KW - Class number

KW - Ono number

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Inequalities of Ono numbers and class numbers associated to imaginary quadratic fields

Abstract

Keywords

ASJC Scopus subject areas

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