Article
| Title: | Weighted Erdős-Kac type theorem over quadratic field in short intervals (English) |
| Author: | Liu, Xiaoli |
| Author: | Yang, Zhishan |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 72 |
| Issue: | 4 |
| Year: | 2022 |
| Pages: | 957-976 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $\mathbb {K}$ be a quadratic field over the rational field and $a_{\mathbb {K}} ( n)$ be the number of nonzero integral ideals with norm $n$. We establish Erdős-Kac type theorems weighted by $a_{\mathbb {K}} (n)^l$ and $a_{\mathbb {K}} (n^2 )^l$ of quadratic field in short intervals with $l\in \mathbb {Z}^{+}$. We also get asymptotic formulae for the average behavior of $a_{\mathbb {K}}(n)^l$ and $a_{\mathbb {K}} ( n^2)^l$ in short intervals. (English) |
| Keyword: | ideal counting function |
| Keyword: | Erdős-Kac theorem |
| Keyword: | quadratic field |
| Keyword: | short intervals |
| Keyword: | mean value |
| MSC: | 11N37 |
| MSC: | 11N45 |
| MSC: | 11N60 |
| idZBL: | Zbl 07655774 |
| idMR: | MR4517587 |
| DOI: | 10.21136/CMJ.2022.0203-21 |
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| Date available: | 2022-11-28T11:32:40Z |
| Last updated: | 2023-04-11 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151121 |
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