New Restriction Estimates for the 3-d Paraboloid over Finite Fields

By Mark Lewko. 2013

47 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/ee4bf8bb1a59bf1bb6febdda0ce0eb3fdf7a0f63

How researchers see this paper

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In Artificial Intelligence

1. Frank de Zeeuw
2. Sophie Stevens

In Discrete Mathematics and Combinatorics

1. Frank de Zeeuw
2. Sophie Stevens

Citations in the corpus

• An improved point‐line incidence bound over arbitrary fields (2016, background): “Finally, we record in this note that our Theorem 3 can be plugged into a result of Lewko [24] to give an improved restriction estimate for the paraboloid in F3p.”