An explicit sum-product estimate in $\mathbb{F}_p$

M. Z. Garaev

An explicit sum-product estimate in $\mathbb{F}_p$

数论 2007-05-23 v1

作者: M. Z. Garaev

摘要

Let $\mathbb{F}_p$ be the field of residue classes modulo a prime number $p$ and let $A$ be a non-empty subset of $\mathbb{F}_p.$ In this paper we give an explicit version of the sum-product estimate of Bourgain, Katz, Tao and Bourgain, Glibichuk, Konyagin on the size of $\max\{|A+A|, |AA|\}.$ In particular, our result implies that if $1<|A|\le p^{7/13}(\log p)^{-4/13},$ then $\max\{|A+A|, |AA|\}\gg \frac{|A|^{15/14}}{(\log|A|)^{2/7}} .$

引用

@article{arxiv.math/0702780,
  title  = {An explicit sum-product estimate in $\mathbb{F}_p$},
  author = {M. Z. Garaev},
  journal= {arXiv preprint arXiv:math/0702780},
  year   = {2007}
}

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11 pages

An explicit sum-product estimate in $\mathbb{F}_p$

摘要

引用

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