## Weighted Erdős-Kac type theorems over Gaussian field in short intervals.(English)Zbl 1474.11169

Summary: Assume that $$\mathbb{K}$$ is Gaussian field, and $$a_{\mathbb{K}}(n)$$ is the number of non-zero integral ideals in $$\mathbb{Z}[i]$$ with norm $$n$$. We establish an Erdős-Kac type theorem weighted by $$a_{\mathbb{K}}(n^2)^l\; (l\in\mathbb{Z}^+)$$ in short intervals. We also establish an asymptotic formula for the average behavior of $$a_{\mathbb{K}}(n^2)^l$$ in short intervals.

### MSC:

 11N60 Distribution functions associated with additive and positive multiplicative functions 11N37 Asymptotic results on arithmetic functions 11N45 Asymptotic results on counting functions for algebraic and topological structures
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### References:

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