Timeline for Estimating the size of set of primes $p$ for which the polynomial is bijective in $\mathbb{F}_p[X]$
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Oct 29, 2021 at 20:01 | comment | added | YCor | How do you define "proportion of polynomials"? It needs to bound both the degrees and coefficients, so this looks very choice-sensitive. | |
| Oct 29, 2021 at 19:57 | history | edited | YCor | CC BY-SA 4.0 |
formatting
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| Oct 29, 2021 at 15:55 | vote | accept | Hhhhhhhhhhh | ||
| Oct 29, 2021 at 14:54 | answer | added | Will Sawin | timeline score: 2 | |
| Oct 29, 2021 at 14:44 | answer | added | David E Speyer | timeline score: 5 | |
| Oct 29, 2021 at 13:51 | comment | added | Hhhhhhhhhhh | Yes exactly @David E Speyer | |
| Oct 29, 2021 at 13:47 | comment | added | David E Speyer | I want to make sure I understand the order of quantifiers here. For a fixed $f$, we define $T_f$ to be the set of primes for which $f(x)$ is bijective modulo $p$. So, if $f(x)= x^3$, then $T_f$ is the primes which are $2 \bmod 3$. In that case, the number of such primes which are $\leq y$ is $\sim \tfrac{y}{2 \log y}$, by the PNT in arithmetic progressions. You want to understand, instead, those polynomials $f$ for which $\#\{ p \in T_f: p \leq y \}$ is $O(\tfrac{y}{(\log y)^2})$. Is that right? | |
| Oct 29, 2021 at 13:43 | history | edited | Hhhhhhhhhhh | CC BY-SA 4.0 |
edited body
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| Oct 29, 2021 at 13:42 | comment | added | Hhhhhhhhhhh | Yes both x are different. I will edit it. | |
| Oct 29, 2021 at 13:41 | comment | added | Will Sawin | Did you mean to have a parameter $x$ controlling the size of the primes which is different from the $x$ used as a variable in the polynomial? | |
| Oct 29, 2021 at 13:06 | history | edited | Hhhhhhhhhhh | CC BY-SA 4.0 |
deleted 20 characters in body; edited title
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| Oct 29, 2021 at 13:00 | history | asked | Hhhhhhhhhhh | CC BY-SA 4.0 |