Timeline for How to use prime number theorem In such cases?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 24, 2022 at 6:48 | comment | added | TravorLZH | From the definition of logarithmic integral, it is natural to believe $\sum_{p\le x}f(p)\approx\int_2^x{f(t)\over\log t}\mathrm dt$ when $f(x)$ is continuously differentiable and satisfies certain other good properties. | |
| Aug 19, 2022 at 22:55 | comment | added | Steven Clark | Did you mean $A(x)=\sum\limits_{k\leq x}f(k)(\pi(k)-\pi(k-1))$? | |
| Aug 19, 2022 at 14:08 | comment | added | davidlowryduda | If $f$ is reasonable (e.g. differentiable), then you can integrate by parts and try to use the prime number theorem to study the other side. Depending on $f$, this may or may not be sufficient to get a good understanding of $A(x)$. Does that make sense? | |
| Aug 19, 2022 at 13:16 | review | Close votes | |||
| Sep 3, 2022 at 3:02 | |||||
| S Aug 19, 2022 at 12:37 | review | First questions | |||
| Aug 19, 2022 at 12:54 | |||||
| S Aug 19, 2022 at 12:37 | history | asked | RAHUL | CC BY-SA 4.0 |