Timeline for Solutions to system of polynomial equations over finite fields
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jun 16, 2020 at 11:09 | answer | added | Ivan Meir | timeline score: 0 | |
| Aug 5, 2015 at 14:45 | comment | added | mrinal | @TerryTao Thanks for the reference. I was thinking more in the regime of constant $d$ and $q$, but $m$ slightly growing with $n$. The dependency on the number of low-degree polynomials needed on $m$ seems quite bad in the paper. | |
| Aug 5, 2015 at 3:26 | comment | added | Terry Tao | In the case when $n$ is very large compared with $d,q,m$, the polynomial regularity lemma and polynomial counting lemma describes, in principle, the equidistribution of $P_1,\dots,P_m$: arxiv.org/abs/0711.3191 . Basically, one has equidistribution unless there are "low rank" obstructions, in that certain linear combinations of $P_1,\dots,P_m$ are expressible in terms of a small number of low-degree polynomials. | |
| Aug 4, 2015 at 20:38 | history | edited | Will Sawin |
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| Aug 4, 2015 at 20:37 | answer | added | Will Sawin | timeline score: 1 | |
| Aug 4, 2015 at 20:15 | comment | added | mrinal | @BorisBukh I meant, do we have good lower bounds on the number of common zeros of a system of low degree homogeneous polynomials over finite fields? If the degree of the polynomials is one, then the number of solutions is $q^{n-r}$, where $r$ is the rank of the system. Are there similar statements for higher degree homogeneous polynomials? | |
| Aug 4, 2015 at 18:59 | comment | added | Boris Bukh | Your question is very broad. Can you perhaps ask a more specific question? Currently, it is not clear even what would constitute an answer to this question. (It is hard to guess the right tool to for your application, if we do not know what it is even approximately.) | |
| Aug 4, 2015 at 18:56 | review | First posts | |||
| Aug 4, 2015 at 20:34 | |||||
| Aug 4, 2015 at 18:46 | history | asked | mrinal | CC BY-SA 3.0 |