### 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.

Original language | English |
---|---|

Pages (from-to) | 307-319 |

Number of pages | 13 |

Journal | Bulletin of the Malaysian Mathematical Sciences Society |

Volume | 40 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2017 |

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### Keywords

- Mertens’ orbit theorem
- Periodic points
- Prime orbit theorem
- The Motzkin shift

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Bulletin of the Malaysian Mathematical Sciences Society*,

*40*(1), 307-319. https://doi.org/10.1007/s40840-015-0144-y

**Analogues of the Prime Number Theorem and Mertens’ Theorem for Closed Orbits of the Motzkin Shift.** / Alsharari, Fahad; Md. Noorani, Mohd. Salmi; Akhadkulov, Habibullah.

Research output: Contribution to journal › Article

*Bulletin of the Malaysian Mathematical Sciences Society*, vol. 40, no. 1, pp. 307-319. https://doi.org/10.1007/s40840-015-0144-y

}

TY - JOUR

T1 - Analogues of the Prime Number Theorem and Mertens’ Theorem for Closed Orbits of the Motzkin Shift

AU - Alsharari, Fahad

AU - Md. Noorani, Mohd. Salmi

AU - Akhadkulov, Habibullah

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

KW - Mertens’ orbit theorem

KW - Periodic points

KW - Prime orbit theorem

KW - The Motzkin shift

UR - http://www.scopus.com/inward/record.url?scp=85008692966&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85008692966&partnerID=8YFLogxK

U2 - 10.1007/s40840-015-0144-y

DO - 10.1007/s40840-015-0144-y

M3 - Article

VL - 40

SP - 307

EP - 319

JO - Bulletin of the Malaysian Mathematical Sciences Society

JF - Bulletin of the Malaysian Mathematical Sciences Society

SN - 0126-6705

IS - 1

ER -