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

Fumio Sairaiji, Kenichi Shimizu

Research output: Contribution to journalArticle

4 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)105-108
Number of pages4
JournalProceedings of the Japan Academy Series A: Mathematical Sciences
Issue number7
Publication statusPublished - 2002 Jan 1
Externally publishedYes



  • Class number
  • Ono's number

ASJC Scopus subject areas

  • Mathematics(all)

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