Inequalities of Ono numbers and class numbers associatedto imaginary quadratic fields

摘要

We denote by h_Dthe class number and byp_Ono of the imaginaryquadratic fields Q('/—D). Sairaiji-Shimizu [2] showed that there are infinitely many imaginaryquadratic fields such that the inequality h_D> C~(PD)holds for any real number. On the other handwe have the possibility that h_D≤c~(PD)holds for infinitely many imaginary quadratic fields for thesame real number c. In this paper, given a real number c, we consider whether h_D≤C~(PD)holds forinfinitely many imaginary quadratic fields or not.