On an Argument of Shkredov on Two-Dimensional Corners
| dc.creator | Lacey, Michael T | |
| dc.creator | McClain, William | |
| dc.date | 2005-10-23 | |
| dc.date | 2007-04-05 | |
| dc.date.accessioned | 2026-07-07T07:55:23Z | |
| dc.date.available | 2026-07-07T07:55:23Z | |
| dc.description | Let $\mathbb F_2^n$ be the finite field of cardinality $2 ^{n}$. For all large $n$, any subset $A\subset \mathbb F_2^n\times \mathbb F_2 ^n$ of cardinality \begin{equation*} \abs{A} \gtrsim 4^n \log\log n (\log n) ^{-1} \end{equation*} must contain three points $ \{(x,y) ,(x+d,y) ,(x,y+d)\}$ for $x,y,d\in \mathbb F_2^n$ and $d\neq0$. Our argument is an elaboration of an argument of Shkredov \cite {math.NT/0405406}, building upon the finite field analog of Ben Green \cite {math.NT/0409420}. The interest in our result is in the exponent on $ \log n$, which is larger than has been obtained previously. | |
| dc.description | 9 pages. IN Online Journal of Analytic Combinatorics, Vol 2. 2007. http://www.ojac.org/vol2/Lacey_McClain_2007.pdf | |
| dc.identifier | https://arxiv.org/abs/math/0510491 | |
| dc.identifier | http://arxiv.org/abs/math/0510491 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/126950 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.title | On an Argument of Shkredov on Two-Dimensional Corners | |
| dc.type | text |