Timeline for Order of elements $\gamma$ and $1-\gamma$ in $\mathbb{F}_q$
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| May 4, 2022 at 7:19 | comment | added | Gabriel Soranzo | Yoou're right: I mean respect the degree | |
| May 4, 2022 at 7:18 | history | edited | Gabriel Soranzo | CC BY-SA 4.0 |
edited body
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| May 3, 2022 at 22:46 | comment | added | LSpice |
I'm confused by the paragraph "As we see here …." As you point out, affine transformations don't respect the order of elements of $\mathbb F_q$ (or even their being non-$0$). Also, why refer to conjugacy classes when $\mathbb F_q$ is Abelian? \\ TeX note: $\mathcal o$ \mathcal o looks the same as $o$ o, so you might want to choose some other symbol.
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| May 3, 2022 at 22:45 | history | edited | LSpice | CC BY-SA 4.0 |
Proofreading; deleted "thanks"
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| May 3, 2022 at 22:14 | comment | added | Will Sawin | The (Weil?) bound for Jacobi sums suggests that the orders of $\gamma$ and $\gamma+1$ behave like independent random variables, so we could expect that any two sufficiently large orders can occur (and can prove this for large-enough orders, depending on the factorizability of $q-1$). | |
| May 3, 2022 at 21:50 | history | asked | Gabriel Soranzo | CC BY-SA 4.0 |