Geodesic
Weighted Erdős-Kac type theorem over quadratic field in short intervals
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 4, pp. 957-976.

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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.
DOI : 10.21136/CMJ.2022.0203-21
Classification : 11N37, 11N45, 11N60
Keywords: ideal counting function; Erdős-Kac theorem; quadratic field; short intervals; mean value 
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     title = {Weighted {Erd\H{o}s-Kac} type theorem over quadratic field in short intervals},
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Liu, Xiaoli; Yang, Zhishan. Weighted Erdős-Kac type theorem over quadratic field in short intervals. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 4, pp. 957-976. doi : 10.21136/CMJ.2022.0203-21. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2022.0203-21/

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