Abstract
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.
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Acknowledgments
The authors would like to acknowledge the grant UKM Grant DIP-2014-034 and Ministry of Education, Malaysia Grant FRGS/1/2014/ST06/UKM/01/1, AP-2013-009, and Modal Insan Berpusat (RAE3) for financial support. The authors also would like to thank the referee for his/her careful reading of the paper and useful suggestions.
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The authors declare that there is no conflict of interests regarding the publication of this article.
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Communicated by Shangjiang Guo.
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Alsharari, F., Noorani, M.S.M. & Akhadkulov, H. Analogues of the Prime Number Theorem and Mertens’ Theorem for Closed Orbits of the Motzkin Shift. Bull. Malays. Math. Sci. Soc. 40, 307–319 (2017). https://doi.org/10.1007/s40840-015-0144-y
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DOI: https://doi.org/10.1007/s40840-015-0144-y