Timeline for Sum of Legendre symbol over primes
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 10, 2018 at 10:23 | vote | accept | Mayank Pandey | ||
| Jun 25, 2018 at 16:50 | comment | added | Wojowu | @WillSawin Woops, you are completely right! It should've been $O(x\exp(-\sqrt{\log X}))$. | |
| Jun 25, 2018 at 16:46 | comment | added | Will Sawin | @Wojowu Are you sure that unconditional estimate is right? It seems stronger than the conditional exponent. You mean a savings of exp root log over the trivial bound? | |
| Jun 25, 2018 at 16:44 | comment | added | Wojowu | I think this is basically equivalent to finding zero-free regions for the Dirichlet L-function associated with the Legendre symbol (which is a Dirichlet character modulo $4d$). Therefore, unconditionally, we have estimates like $O(\exp(\sqrt{\log X}))$, while conjecturally $O(X^{1/2+\varepsilon})$. | |
| Jun 25, 2018 at 16:38 | answer | added | GH from MO | timeline score: 3 | |
| Jun 25, 2018 at 8:58 | comment | added | Stanley Yao Xiao | The Duke-Friedlander-Iwaniec paper seems relevant: jstor.org/stable/2118527?seq=1#page_scan_tab_contents | |
| Jun 25, 2018 at 8:10 | history | asked | Mayank Pandey | CC BY-SA 4.0 |