Timeline for Summatory functions for fractional parts
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Aug 28, 2022 at 3:05 | comment | added | Wlod AA | Well, my numerical experiment tells me that you, GH, are right. | |
| Aug 28, 2022 at 0:11 | comment | added | Wlod AA | however, GH, I was stressing word locally. The smoothness of the estimate seems to be a global result. | |
| Aug 28, 2022 at 0:05 | comment | added | GH from MO | @WlodAA: The arithmetic nature of $n$ does not influence your functions $\tau$ and $\xi$ too much. For example, your $\tau(n)$ is really $\sum_{k=1}^n n/k-\sigma(n)$, which by my last display is $(1-\gamma)n+O_\varepsilon(n^{131/416+\varepsilon})$ for any $\varepsilon>0$. | |
| Aug 27, 2022 at 23:51 | comment | added | Wlod AA | Sorry for (temporarily) forgetting about the standard fractional part notation. I'll correct it. #### The local domination mentioned in my Q. has a good chance to be at least partially true. | |
| Aug 27, 2022 at 23:50 | history | edited | GH from MO | CC BY-SA 4.0 |
added 327 characters in body
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| Aug 27, 2022 at 23:48 | comment | added | GH from MO | @WlodAA See my "Added" section. Sorry about the mismatch in notation. | |
| Aug 27, 2022 at 23:44 | comment | added | Wlod AA | My earlier (removed by me) Q. had $\ \prod\ $ instead of $\ \sum.\ $ Possibly, IPJ-functions from my removed post are new or relatively new -- possibly, they have some research potential. | |
| Aug 27, 2022 at 23:33 | vote | accept | Wlod AA | ||
| Aug 27, 2022 at 22:08 | history | edited | GH from MO | CC BY-SA 4.0 |
added 121 characters in body
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| Aug 27, 2022 at 22:01 | history | answered | GH from MO | CC BY-SA 4.0 |