تقرير
An elementary Tauberian proof of the Prime Number Theorem
| العنوان: | An elementary Tauberian proof of the Prime Number Theorem |
|---|---|
| المؤلفون: | Angot, Philippe |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, Mathematics - History and Overview, 11A41, 11M45, 40A05, 40E05, 44A10 (primary), 11N05, 30B50, 42A38 (secondary) |
| الوصف: | We give a simple Tauberian proof of the Prime Number Theorem using only elementary real analysis. Hence, the analytic continuation of Riemann's zeta function $\zeta$ and its non-vanishing value on the whole line $\{z\in {\mathbb C};\,{\mathrm{Re}\,} z=1\}$ are no more required. This is achieved by showing a strong extension for Laplace transforms on the real line of Wiener--Ikehara's theorem on Dirichlet's series, where the Tauberian assumption is reduced to a local boundary behavior around the pole. Comment: 9 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2404.13019 |
| رقم الأكسشن: | edsarx.2404.13019 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |