Garaev's Inequality in finite fields not of prime order
Number Theory
2007-05-23 v1 Classical Analysis and ODEs
Abstract
We prove a version of Garaev's sum product theorem in the set of finite fields with non-prime order. Because of the presence of subfields, this seems to require some hypotheses on the set. We work under a condition analogous to having Hausdorff dimension less than 1/2. Under these conditions, we obtain a sum-product theorem with exponent 49/48.
Cite
@article{arxiv.math/0703676,
title = {Garaev's Inequality in finite fields not of prime order},
author = {Nets Hawk Katz and Chun-Yen Shen},
journal= {arXiv preprint arXiv:math/0703676},
year = {2007}
}
Comments
8 pages