تقرير
Sharper bounds for the error term in the Prime Number Theorem
| العنوان: | Sharper bounds for the error term in the Prime Number Theorem |
|---|---|
| المؤلفون: | Fiori, Andrew, Kadiri, Habiba, Swidinsky, Joshua |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, 11A05, 11N25, 11M06, 11N56, 11M26 |
| الوصف: | We provide very effective methods to convert both asymptotic and explicit numeric bounds on the prime counting function $\psi(x)$ to bounds of the same type on both $\theta(x)$ and $\pi(x)$. This follows up our previous work on $\psi(x)$ in \cite{FKS}, and prove that $ | \pi(x) - \mathrm{Li}(x) | \leq 9.2211\, x\sqrt{\log(x)} \exp \big( -0.8476 \sqrt{\log(x)} \big) $ for all $x\ge 2$. Additionally, we are able to obtain the best numeric bounds for $x$ on a very large interval (all $x$ up to $\exp(1.8\cdot10^9)$). Comment: 19 pages with 7 tables, see previous arxiv version for ancillary file (167 pages) which includes more detailed tables |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2206.12557 |
| رقم الأكسشن: | edsarx.2206.12557 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |