Timeline for Inequality with slowly varying functions
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 31, 2022 at 0:22 | vote | accept | zxmkn | ||
| May 30, 2022 at 16:55 | comment | added | Iosif Pinelis | @zxmkn : This follows because $f$ and $\ell$ are slowly varying functions, and for any slowly varying function $L$ we have $L(n)=n^{o(1)}$, by the Karamata representation theorem (en.wikipedia.org/wiki/… ). You can also directly show that $\ln(f(n)\ell(n))=o(\ln n)$, which is equivalent to what you are asking here about. | |
| May 30, 2022 at 15:13 | comment | added | zxmkn | @IosifPinelis : Could you explain how to get the representation $a_n = n^{1/\alpha +o(1)}$? Namely, how can we see that $[\log^2 n \cdot \exp(b \sqrt{\log n})]^{1/\alpha} = n^{o(1)}$? | |
| May 30, 2022 at 14:09 | comment | added | Iosif Pinelis | @zxmkn : All right. Please let me know if some of the steps need further details. | |
| May 30, 2022 at 13:40 | comment | added | zxmkn | @IosifPinelis : Thank you for your help! I'm working through the details right now and will accept your answer once I verify everything. | |
| May 30, 2022 at 13:31 | comment | added | Iosif Pinelis | @zxmkn : Do you have a response to the answer below? | |
| May 29, 2022 at 17:30 | comment | added | fedja | @IosifPinelis Then you fried the author :-) | |
| May 29, 2022 at 16:57 | comment | added | Iosif Pinelis | @fedja : The definition of a slowly varying function $\ell$ in the paper is the standard one: $\ell(tx)\sim\ell(t)$ as $t\to\infty$ for each $x>0$. This is formula (1.6) in the paper. | |
| May 29, 2022 at 16:14 | comment | added | fedja | It all depends on the exact definition of "slowly varying". So, what is it in the paper? | |
| May 29, 2022 at 2:54 | answer | added | Iosif Pinelis | timeline score: 2 | |
| S May 28, 2022 at 12:20 | review | First questions | |||
| May 28, 2022 at 12:59 | |||||
| S May 28, 2022 at 12:20 | history | asked | zxmkn | CC BY-SA 4.0 |