| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2022-11-28T11:32:40Z |
| Last updated:
|
2025-01-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151121 |
| . |
| Reference:
|
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| . |
