Counting primes by sums of frequencies
| Autor: | Miralles, Alejandro, Torres, Damià |
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| Rok vydání: | 2016 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We introduce the sequence $(a_n) \subset (0,1]$ and prove that the asymptotic behaviour of $\sum_{k=1}^n a_k$ is the same than $\pi(n)$, the prime-counting function. We also obtain that $\pi(n) \sim n a_n$ and we estimate $\frac{1}{a_n}-\frac{n}{\pi(n)}$ showing that $\lim_{n \rightarrow \infty} \frac{1}{a_n}-\frac{n}{\pi(n)}$ is convergent. |
| Databáze: | arXiv |
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