| Reference : The $n$-th prime asymptotically |
| Scientific journals : Article | |||
| Physical, chemical, mathematical & earth Sciences : Mathematics | |||
| http://hdl.handle.net/10993/18415 | |||
| The $n$-th prime asymptotically | |
| English | |
Arias de Reyna, Juan  [] | |
| Toulisse, Jérémy [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] | |
| 2013 | |
| Journal de Théorie des Nombres de Bordeaux | |
| Université de Bordeaux. Centre de Recherches Mathématiques | |
| Yes (verified by ORBilu) | |
| 1246-7405 | |
| Talence | |
| France | |
| [en] A new derivation of the classic asymptotic expansion
of the n-th prime is presented. A fast algorithm for the compu- tation of its terms is also given, which will be an improvement of that by Salvy (1994). Realistic bounds for the error with $li−1 (n)$, after having re- tained the first $m$ terms, for $1 ≤ m ≤ 11$, are given. Finally, as- suming the Riemann Hypothesis, we give estimations of the best possible $r_3$ such that, for $n ≥ r_3$ , we have $p_n > s_3 (n)$ where $s_3 (n)$ is the sum of the first four terms of the asymptotic expansion. | |
| http://hdl.handle.net/10993/18415 |
| File(s) associated to this reference | ||||||||||||||
|
Fulltext file(s):
| ||||||||||||||
All documents in ORBilu are protected by a user license.
