Large and moderate deviation principles for the Erdős-Kac theorem in function fields
type: Item
instance of: scholarly article
title: Large and moderate deviation principles for the Erdős-Kac theorem in function fields
zbMATH Open document ID: 1465.11172
author: Tingting Feng
author: Shaochen Wang
author: Guangyu Yang
published in: Statistics \& Probability Letters
publication date: 2020-10-12T00:00:00Z
review text: Let \(U_n\) be a random integer chosen uniformly from \(\{1, 2,\dots, n\}\) and \(X_n\) denote the number of distinct prime divisors of \(U_n\). Erdős-Kac theorem asserts that, for any \(a<b\), \[ \lim_{n\to\infty}\mathbf{P}\left(\frac{X_n-\log\log n}{\sqrt{\log\log n}}\in(a,b]\right)=\frac{1}{\sqrt{2\pi}}\int_a^b e^{-\frac{x^2}{2}}dx. \] In the paper under review the authors prove the large and moderate deviation principles for the Erdős-Kac theorem in the polynomial rings of finite fields.
reviewed by: Mehdi Hassani
Mathematics Subject Classification ID: 11K65
Mathematics Subject Classification ID: 11N60
Mathematics Subject Classification ID: 11R58
Mathematics Subject Classification ID: 60F10
zbMATH DE Number: 7259032
zbMATH Keywords: Erdős-Kac theorem
zbMATH Keywords: finite fields
zbMATH Keywords: large deviation principle
zbMATH Keywords: polynomial rings
MaRDI profile type: Publication
full work available at URL: j.spl.2020.108780
OpenAlex ID: W3017289212
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DOI: 10.1016/J.SPL.2020.108780
description: scientific article; zbMATH DE number 7259032