Timeline for On the connection between $\pi(x)-Li(x)$ and $\theta(x)-x$
Current License: CC BY-SA 4.0
5 events
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| Aug 18, 2019 at 16:52 | comment | added | Greg Martin | RH certainly implies this, since both differences individually are $\ll\sqrt x\log^2x$ under RH. But $\pi(x)-\mathop{\rm Li}(x)$ is going to act like $1/\log x$ times $\theta(x)-x$; so morally speaking, the difference between the two differences will be as big as $\theta(x)-x$ itself, which is definitely not $\ll\sqrt x\log^2x$ if RH is false. So I think it is equivalent to RH. But I know this isn't a proof. | |
| Aug 18, 2019 at 14:12 | comment | added | reuns | Partial summation | |
| Aug 18, 2019 at 7:17 | history | edited | Q_p | CC BY-SA 4.0 |
added 4 characters in body; edited title
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| Aug 18, 2019 at 7:05 | review | First posts | |||
| Aug 18, 2019 at 10:01 | |||||
| Aug 18, 2019 at 7:04 | history | asked | Q_p | CC BY-SA 4.0 |