Timeline for Correlations of $\phi(n)/n$
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 22, 2021 at 10:18 | history | bounty ended | Dr. Pi | ||
| Mar 15, 2021 at 9:24 | history | edited | A of E | CC BY-SA 4.0 |
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| Mar 10, 2021 at 19:46 | comment | added | Dr. Pi | @Sungjin Kim : indeed you are right, I corrected it-thank you for the comment. | |
| Mar 10, 2021 at 18:11 | comment | added | Sungjin Kim | @AofE I am wondering about the same thing. I will be great if you can elaborate on Poisson summation part, how Siegel-Walfisz and large sieve work here, and how to use DFI result. The current best error term on unsmoothed sum $\sum_{n\leq x} \phi(n)/n$ has $O(\log^{2/3} x (\log\log x)^{4/3})$. | |
| Mar 10, 2021 at 18:09 | comment | added | Sungjin Kim | @Dr.Pi I think the secondary term of $\sum_{n\leq x} \phi(n)/n w(n/x)$ might be $c_1(w) \log x$ and error is $o(\log x)$. You wrote $\log^2 x$ in your post. | |
| Mar 10, 2021 at 17:59 | comment | added | Dr. Pi | That is great, many thanks! I was wondering why there is no secondary term here but there is a secondary term in the simpler sum $\sum_{n\leq x } \phi(n)/n w(n/x)$? Is it because of exponential sums machinery? | |
| Mar 10, 2021 at 16:55 | history | edited | A of E | CC BY-SA 4.0 |
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| Mar 10, 2021 at 16:55 | review | First posts | |||
| Mar 10, 2021 at 16:59 | |||||
| Mar 10, 2021 at 16:49 | history | answered | A of E | CC BY-SA 4.0 |