| 高斯域上理想计数函数在短区间上的Erdös-Kac型定理 |
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| 引用本文： | 刘晓莉,杨志善. 高斯域上理想计数函数在短区间上的Erdös-Kac型定理[J]. 数学学报, 2021, 64(1): 65-76 |
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| 作者姓名： | 刘晓莉 杨志善 |
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| 作者单位： | 青岛大学数学与统计学院 青岛 266071 |
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| 摘 要： | 设aK(n)为Z[i]中范数为n的非零整理想个数,l∈Z+,本文给出了短区间上权为ak(n)l的Erdos-Kac型定理,并得到短区间上aK(n)l均值估计的渐近公式.
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| 关 键 词： | 理想计数函数 Erd?s-Kac定理 高斯域 短区间 均值估计 |
Erdös–Kac Type Theorem for Ideal Counting Function over Gaussian Field in Short Intervals |
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| Xiao Li LIU,Zhi Shan YANG. Erdös–Kac Type Theorem for Ideal Counting Function over Gaussian Field in Short Intervals[J]. Acta Mathematica Sinica, 2021, 64(1): 65-76 |
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| Authors: | Xiao Li LIU Zhi Shan YANG |
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| Affiliation: | School of Mathematics and Statistics, Qingdao University, Qingdao 266071, P. R. China |
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| Abstract: | Let aK(n) be the number of non-zero integral ideals in Z[i] with norm n, l ∈ Z+. In this paper, we establish an Erdös-Kac type theorem with weight aK(n)l in short intervals, and we get an asymptotic formula for the average behavior of aK(n)l in short intervals. |
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| Keywords: | ideal counting function Erdös-Kac theorem Gaussian field short intervals mean value estimate |
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