On an Argument of Shkredov on Two-Dimensional Corners
On an Argument of Shkredov on Two-Dimensional Corners
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论二维角上什克列多夫的论证
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发表时间：
2005
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通讯作者：
William McClain
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作者：
M. Lacey;William McClain
设Fn是基数为2n的有限域.对于所有大的n，任何子集A！F n“F n的基数|一| ! 4 n loglogn logn，必须包含三个点{（x，y），（x + d，y），（x，y + d）}对于x，y，d # F n和d $0。我们的论证是对Shkredov [14]论证的一种阐述，建立在Ben绿色[10]的有限域模拟之上。在我们的结果的兴趣是在对数的指数，这是大于已获得先前。
Let F n be the finite field of cardinality 2 n . For all large n, any subset A ! F n " F n of cardinality |A| ! 4 n loglogn logn , must contain three points {(x,y),(x + d,y),(x,y + d)} for x,y,d # F n and d $ 0. Our argument is an elaboration of an argument of Shkredov [14], building upon the finite field analog of Ben Green [10]. The interest in our result is in the exponent on logn, which is larger than has been obtained previously.