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.
Rudnev, On the number of incidences between points and planes in thre e dimensions , Combinatorica 38 (2018): 219–54
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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.