Garaev's Inequality in finite fields not of prime order

Details Garaev's Inequality in finite fields not of prime order Garaev's Inequality in finite fields not of prime order

2007-03-22

arxiv.org/abs/math/0703676v1

Mathematics

Number Theory

8 pages

Scientific paper

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.

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