Timeline for Upper and lower bounds of sequences whose product of terms is asymptotically equal to their arithmetic mean
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Apr 26, 2018 at 20:09 | vote | accept | Sylvain JULIEN | ||
| Apr 26, 2018 at 16:36 | comment | added | Iosif Pinelis | Concerning that MSE question, I am not familiar enough with number theory to answer it. | |
| Apr 26, 2018 at 16:31 | comment | added | Sylvain JULIEN | I see. As far as the question on MSE is concerned, would it strongly suggest that the constant involved in $ O(\log^{2}n) $ is $ 1 $, as it should be equal to $ 1/\inf_{k\leq m}\{c_{k}\} $? | |
| Apr 26, 2018 at 16:19 | comment | added | Iosif Pinelis | @SylvainJULIEN : Yes, that is right. I have added a brief remark about the main idea of the proof: that the consecutive arithmetic means may only vary very slowly, whereas the consecutive products may vary very fast (if factors bounded away from $1$ are allowed). | |
| Apr 26, 2018 at 16:13 | history | edited | Iosif Pinelis | CC BY-SA 3.0 |
added 142 characters in body
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| Apr 26, 2018 at 16:10 | comment | added | Sylvain JULIEN | Thank you. So if I understand correctly, the only possible way for a corridor sequence to exist is to allow the interval $[1,1] $? | |
| Apr 26, 2018 at 15:29 | history | edited | Iosif Pinelis | CC BY-SA 3.0 |
added 116 characters in body
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| Apr 26, 2018 at 15:19 | history | answered | Iosif Pinelis | CC BY-SA 3.0 |