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Weighted Erdős–Kac Type Theorems Over Gaussian Field In Short Intervals

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Qingdao University, Qingdao, 266071, P. R. China

    X.-L. Liu & Z.-S. Yang

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  1. X.-L. Liu
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  2. Z.-S. Yang
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Correspondence to Z.-S. Yang.

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Liu, XL., Yang, ZS. Weighted Erdős–Kac Type Theorems Over Gaussian Field In Short Intervals. Acta Math. Hungar. 162, 465–482 (2020). https://doi.org/10.1007/s10474-020-01087-6

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  • DOI: https://doi.org/10.1007/s10474-020-01087-6

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