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

Fahad Alsharari, Mohd. Salmi Md. Noorani, Habibullah Akhadkulov

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)307-319
Number of pages13
JournalBulletin of the Malaysian Mathematical Sciences Society
Volume40
Issue number1
DOIs
Publication statusPublished - 1 Jan 2017

Fingerprint

Prime number theorem
Closed Orbit
Orbit
Analogue
Direct Method
Theorem
Asymptotic Formula
Riemann zeta function
Dynamical system

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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

In: Bulletin of the Malaysian Mathematical Sciences Society, Vol. 40, No. 1, 01.01.2017, p. 307-319.

Research output: Contribution to journalArticle

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