Geodesic
Weighted Erdős-Kac type theorem over quadratic field in short intervals
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 4, pp. 957-976 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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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     author = {Liu, Xiaoli and Yang, Zhishan},
     title = {Weighted {Erd\H{o}s-Kac} type theorem over quadratic field in short intervals},
     journal = {Czechoslovak Mathematical Journal},
     pages = {957--976},
     year = {2022},
     volume = {72},
     number = {4},
     doi = {10.21136/CMJ.2022.0203-21},
     mrnumber = {4517587},
     zbl = {07655774},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2022.0203-21/}
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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

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