Establishes L^2 to L^r bound with r > 32/9 for the Fourier extension operator on the 3D paraboloid over finite fields of odd characteristic where -1 is nonsquare, via bilinear estimates from a geometric decomposition of point sets into controlled rectangles or trapezoids.
Lewko, Counting rectangles and an improved restriction estimate f or the paraboloid in F 3 p , Proceedings of the American Mathematical Society 148 (4), 1535–1543
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A bilinear approach to the finite field restriction problem
Establishes L^2 to L^r bound with r > 32/9 for the Fourier extension operator on the 3D paraboloid over finite fields of odd characteristic where -1 is nonsquare, via bilinear estimates from a geometric decomposition of point sets into controlled rectangles or trapezoids.