We denote by hD the class number and by pD the Ono number of the imaginary quadratic fields Q(√-D). Sairaiji-Shimizu  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.
|ジャーナル||Proceedings of the Japan Academy Series A: Mathematical Sciences|
|出版ステータス||Published - 2009 4|
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