On the restriction problem for discrete paraboloid in lower dimension

Abstract

We apply geometric incidence estimates in positive characteristic to prove the optimal $L^2\to L^3$ Fourier extension estimate for the paraboloid in the four-dimensional vector space over a prime residue field. In three dimensions, when $-1$ is not a square, we prove an $L^2\to L^{\frac{32}{9}}$ extension estimate, improving the previously known exponent $\frac{68}{19}.$

Final version

References in corpus (1)

• New results on sum-product type growth over fields

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