Sum-product phenomena in F_p: a brief introduction
Sum-product phenomena in F_p: a brief introduction
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F_p 中的和积现象：简介
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发表时间：
2009
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通讯作者：
B. Green
中科院分区：
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作者：
B. Green
这些笔记来自于我在2009年四旬期上的剑桥第三部分加法组合学课程。其目的是了解最简单的证明的Bourgain-Glibichuk-Konyagin界指数和子群。作为一个副产品，人们得到了一个干净的证明Bourgain-Katz-Tao定理的和产品的现象在F_p。参数基本上是从一份文件中提取Bourgain，我受益匪浅，收到未发表的课程笔记Elon Lindenstrauss。没有原创性。
These notes arose from my Cambridge Part III course on Additive Combinatorics, given in Lent Term 2009. The aim was to understand the simplest proof of the Bourgain-Glibichuk-Konyagin bounds for exponential sums over subgroups. As a byproduct one obtains a clean proof of the Bourgain-Katz-Tao theorem on the sum-product phenomenon in F_p. The arguments are essentially extracted from a paper of Bourgain, and I benefitted very much from being in receipt of unpublished course notes of Elon Lindenstrauss. No originality is claimed.