Weighted Erdős-Kac type theorem over quadratic field in short intervals

Liu, Xiaoli, and Yang, Zhishan. "Weighted Erdős-Kac type theorem over quadratic field in short intervals." Czechoslovak Mathematical Journal 72.4 (2022): 957-976. <http://eudml.org/doc/298910>.

@article{Liu2022,
abstract = {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.},
author = {Liu, Xiaoli, Yang, Zhishan},
journal = {Czechoslovak Mathematical Journal},
keywords = {ideal counting function; Erdős-Kac theorem; quadratic field; short intervals; mean value},
language = {eng},
number = {4},
pages = {957-976},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Weighted Erdős-Kac type theorem over quadratic field in short intervals},
url = {http://eudml.org/doc/298910},
volume = {72},
year = {2022},
}

TY - JOUR
AU - Liu, Xiaoli
AU - Yang, Zhishan
TI - Weighted Erdős-Kac type theorem over quadratic field in short intervals
JO - Czechoslovak Mathematical Journal
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 72
IS - 4
SP - 957
EP - 976
AB - 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.
LA - eng
KW - ideal counting function; Erdős-Kac theorem; quadratic field; short intervals; mean value
UR - http://eudml.org/doc/298910
ER -