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International Mathematics Research Notices (2007) Vol. 2007 : article ID rnm007, 14 pages, doi:10.1093/imrn/rnm007 published on Jun 17, 2007
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Copyright © The Author 2007. Published by Oxford University Press.

Sum-product Estimates in Finite Fields via Kloosterman Sums

Derrick Hart1, Alex Iosevich1, and Jozsef Solymosi2

1 Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211
2 Department of Mathematics, University of British Columbia 1984 Mathematics Road, Vancouver, BC, Canada V6T 1Z2

Correspondence: Correspondence to be sent to: Alex Iosevich, Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211, USA. e-mail: iosevich{at}math.missouri.edu

We establish improved sum-product bounds in finite fields using incidence theorems based on bounds for classical Kloosterman and related sums.

Communicated by Jean Bourgain


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