| Autor: |
Tong Wei |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
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| Zdroj: |
AIMS Mathematics, Vol 9, Iss 3, Pp 5863-5876 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
2473-6988 |
| DOI: |
10.3934/math.2024285?viewType=HTML |
| Popis: |
Let $ O_{K} = \mathbb{Z}[i] $. For each positive integer $ n $, denote $ \xi_{K}(n) $ as the number of integral ideals whose norm divides $ n $ in $ O_{K} $. In this paper, we studied the distribution of ideals whose norm divides $ n $ in $ O_{K} $ by using the Selberg-Delange method. This is a natural variant of a result studied by Deshouillers, Dress, and Tenenbaum (often called the DDT Theorem), and we found that the distribution function was subject to beta distribution with density $ \sqrt{3}/(2\pi\sqrt[3]{u^{2}(1-u)}) $. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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