Abstract
We denote by $h_{D}$ the class number and by $p_{D}$ the Ono number of the imaginary quadratic fields $\mathbf{Q}(\sqrt{-D})$. Sairaiji-Shimizu [2] showed that there are infinitely many imaginary quadratic fields such that the inequality $h_{D} >c^{ p_{D}}$ holds for any real number. On the other hand we have the possibility that $h_{D} \leqq c^{ p_{D}}$ holds for infinitely many imaginary quadratic fields for the same real number $c$. In this paper, given a real number $c$, we consider whether $h_{D} \leqq c^{ p_{D}}$ holds for infinitely many imaginary quadratic fields or not.
Citation
Kenichi Shimizu. "Inequalities of Ono numbers and class numbers associated to imaginary quadratic fields." Proc. Japan Acad. Ser. A Math. Sci. 85 (4) 46 - 48, April 2009. https://doi.org/10.3792/pjaa.85.46
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