Asymptotic of summation functions
| Autor: | Volfson, Victor |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We will study the asymptotic behavior of summation functions of a natural argument, including the asymptotic behavior of summation functions of a prime argument in the paper. A general formula is obtained for determining the asymptotic behavior of the sums of functions of a prime argument based on the asymptotic law of primes. We will show, that under certain conditions: $\sum_{p \leq n} {f(p)}= \sum_{k=2}^n {\frac {f(k)}{\log(k)}(1+o(1))}$, where $p$ is a prime number. In the paper, the necessary and sufficient conditions for the fulfillment of this formula are proved. Comment: 15 pages |
| Databáze: | arXiv |
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