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Mertensโ Theorem for some certain intermediate growths |
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| รหัสดีโอไอ | |
| Creator | Sawian Jaidee |
| Title | Mertensโ Theorem for some certain intermediate growths |
| Publisher | Research and Development Office, Prince of Songkla University |
| Publication Year | 2565 |
| Journal Title | Songklanakarin Journal of Science an Technology (SJST) |
| Journal Vol. | 44 |
| Journal No. | 1 |
| Page no. | 201-209 |
| Keyword | prime numbers, closed orbits, periodic points, Mertensโ Theorem, S-integer dynamical systems |
| URL Website | https://rdo.psu.ac.th/sjst/index.php |
| ISSN | 0125-3395 |
| Abstract | The dynamical Mertens' Theorem gives asymptotics for weighted averages of numbers of closed orbits in S-integerdynamical systems, which are constructed from arithmetic data, namely , , and S a subset of rational primes. Theway of finding such asymptotic expressions is an analogue of Mertensโ Theorem in analytic number theory. In this article, wefocus on the dynamical Mertens' Theorem of some certain growths in case S and its complement are infinite subsets of allrational primes. More precisely, our aim is to find out a leading coefficient which comes from the main term in the asymptoticexpression of our interested setting. Moreover, the real interval covering such a coefficient will be provided in some certainexamples. |
