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PDF(442 KB)
PDF(442 KB)
高斯域上理想计数函数在短区间上的Erdös-Kac型定理
Erdös–Kac Type Theorem for Ideal Counting Function over Gaussian Field in Short Intervals
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Erdös-Kac型定理，并得到短区间上aK（n）l均值估计的渐近公式.
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.
理想计数函数 / Erdö / s-Kac定理 / 高斯域 / 短区间 / 均值估计 {{custom_keyword}} /
ideal counting function / Erdös-Kac theorem / Gaussian field / short intervals / mean value estimate {{custom_keyword}} /
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