Analogues of the Prime Number Theorem and Mertens’ Theorem for Closed Orbits of the Motzkin Shift

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• 作者：Fahad Alsharari ; Mohd Salmi Md Noorani…
• 关键词：The Motzkin shift ; Periodic points ; Prime orbit theorem ; Mertens’ orbit theorem
• 刊名：Bulletin of the Malaysian Mathematical Sciences Society
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：40
• 期：1
• 页码：307-319
• 全文大小：
• 刊物类别：Mathematics, general; Applications of Mathematics;
• 刊物主题：Mathematics, general; Applications of Mathematics;
• 出版者：Springer Singapore
• ISSN：2180-4206
• 卷排序：40

文摘

In this paper, the prime orbit theorem and Mertens’ orbit theorem are proved for a shift dynamical system of infinite type called the Motzkin shift. Instead of using the zeta function approach to find the asymptotic formulas, different and more direct methods are used in the proof without any complicated theoretical discussion.