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New Restriction Estimates for the 3-d Paraboloid over Finite Fields (1302.6664v2)
Published 27 Feb 2013 in math.CA and math.CO
Abstract: We improve the range of exponents for the restriction problem for the 3-d paraboloid over finite fields. The key new ingredient is a variant of the Bourgain-Katz-Tao finite field incidence theorem derived from sum-product estimates. In prime order fields, we give an explicit relationship between the exponent in this incidence theorem and restriction estimates for the paraboloid.