The Finite Field Restriction Problem for the Paraboloid
Prior state unknown→proved
a record exponent; the conjectured range is not yet reached
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analysis / Harmonic analysis
The Finite Field Restriction Problem for the Paraboloid
For the three-dimensional paraboloid $P_3$ over a prime field in which $-1$ is not a square, the Fourier extension operator maps $L^2$ to $L^r$ for $r > 176/51 = 3.45098\ldots$, improving the exponent by combining a bilinear approach with point-line incidence bounds.
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For the three-dimensional paraboloid $P_3$ over a prime field in which $-1$ is not a square, the Fourier extension operator maps $L^2$ to $L^r$ for $r > 176/51 = 3.45098\ldots$, improving the exponent by combining a bilinear approach with point-line incidence bounds.
a record exponent; the conjectured range is not yet reached
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