Frontiers of Mathematics in China >

2019 , Vol. 14 >Issue 6: 1303 - 1316

DOI: https://doi.org/10.1007/s11464-019-0808-2

RESEARCH ARTICLE

Generalization of Erdős-Kac theorem

  • Yalin SUN , 1 ,
  • Lizhen WU 2
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  • 1. School of Mathematical Sciences, East China Normal University, Shanghai 200241, China
  • 2. School of Mathematical Sciences and Statistics, Henan University, Kaifeng 475004, China

Received date: 23 Aug 2019

Accepted date: 14 Dec 2019

Published date: 15 Dec 2019

Copyright

2019 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature
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Abstract

Let ω(n) is the number of distinct prime factors of the natural number n,we consider two cases where ℓ is even and odd natural numbers, and then we prove a more general form of the classical Erdős-Kac theorem.

Key words： Erdős-Kac theorem; central limit theorem; value distribution

Cite this article

Yalin SUN , Lizhen WU . Generalization of Erdős-Kac theorem[J]. Frontiers of Mathematics in China, 2019 , 14(6) : 1303 -1316 . DOI: 10.1007/s11464-019-0808-2

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