Dynamics on the number of prime divisors for additive arithmetic semigroups
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Publication:2135564
DOI10.1016/J.FFA.2022.102029zbMATH Open1497.37009arXiv2109.11290OpenAlexW3199594554WikidataQ114179454 ScholiaQ114179454MaRDI QIDQ2135564
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Publication date: 9 May 2022
Published in: (Search for Journal in Brave)
Abstract: In 2020, Bergelson and Richter gave a dynamical generalization of the classical Prime Number Theorem, which has been generalized by Loyd in a disjoint form with the ErdH{o}s-Kac Theorem. These generalizations reveal the rich ergodic properties of the number of prime divisors of integers. In this article, we show a new generalization of Bergelson and Richter's Theorem in a disjoint form with the distribution of the largest prime factors of integers. Then following Bergelson and Richter's techniques, we will show the analogues of all of these results for the arithmetic semigroups arising from finite fields as well.
Full work available at URL: https://arxiv.org/abs/2109.11290
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