Timeline for A (simple) polynomial congruence to modulus prime power
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 24, 2020 at 17:48 | vote | accept | tomos | ||
| Sep 23, 2020 at 9:35 | vote | accept | tomos | ||
| Sep 24, 2020 at 17:48 | |||||
| Sep 20, 2020 at 18:45 | comment | added | Servaes | Also, for the differentiability condition for Hensel's lemma to hold, it is necessary that $p$ doesn't divide $n$, and that $p$ doesn't divide $R$. | |
| Sep 20, 2020 at 18:37 | comment | added | Servaes | So when you say that the number $N(n,p^{\alpha},R)$ of solutions to the congruence $$x^n\equiv R\pmod{p^\alpha},$$ satisfies $N(n,p^{\alpha},R)\ll_n1$, you mean to say that $$N(n,p^{\alpha},R)\leq C(n),$$ for some function depending only on $n$? | |
| Sep 20, 2020 at 18:34 | answer | added | Servaes | timeline score: -1 | |
| Sep 20, 2020 at 18:25 | comment | added | tomos | sorry, i mean: If in context we have variables $v_1,...,v_n,u_1,...,u_m$ and functions $f,g$ with $g$ positive, then $f(v_1,...,v_n)\ll _{u_1,...,u_m}g(v_1,...,v_n)$ means $|f(v_1,...,v_n)|\leq C_{u_1,...,u_m}g(v_1,...,v_n)$ for some positive constant $C$ independent of $v_1,...,v_n$ but dependent possibly on $u_1,...,u_m$ | |
| Sep 20, 2020 at 18:20 | comment | added | Servaes | I still don't understand what you mean by that symbol, or that sentence. | |
| Sep 20, 2020 at 18:19 | comment | added | tomos | independent of $p,\alpha $ | |
| Sep 20, 2020 at 18:16 | comment | added | Servaes | What do you mean by "...has $\ll _n1$ solutions..."? | |
| Sep 20, 2020 at 17:55 | history | asked | tomos | CC BY-SA 4.0 |