An elementary Tauberian proof of the Prime Number Theorem
| Autor: | Angot, Philippe |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 |
| Databáze: | arXiv |
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