Comparing the number of ideals in quadratic number fields
| Autor: | Qian Wang, Xue Han |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Mathematical Modelling and Control, Vol 2, Iss 4, Pp 268-271 (2022) |
| Druh dokumentu: | article |
| ISSN: | 2767-8946 |
| DOI: | 10.3934/mmc.2022025?viewType=HTML |
| Popis: | Denote by $ a_{K}(n) $ the number of integral ideals in $ K $ with norm $ n $, where $ K $ is a algebraic number field of degree $ m $ over the rational field $ \mathcal{Q} $. Let $ p $ be a prime number. In this paper, we prove that, for two distinct quadratic number fields $ K_i = \mathcal{Q}(\sqrt{d_i}), \ i = 1, 2 $, the sets both $ \{p\ |\ a_{K_1}(p)< a_{K_2}(p)\} \text{ and } \{p\ |\ a_{K_1}(p^2)< a_{K_2}(p^2)\} $ have analytic density $ 1/4 $, respectively. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|