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arXiv:math/0703676 [math.NT]AbstractReferencesReviewsResources

Garaev's Inequality in finite fields not of prime order

Nets Hawk Katz, Chun-Yen Shen

Published 2007-03-22Version 1

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.

Comments: 8 pages
Categories: math.NT, math.CA
Subjects: 11T99, 05D99
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