Mockenhaupt–Tao finite-field restriction conjecture

Prove that, for every prime p congruent to 3 modulo 4, the finite-field restriction estimate R^*(2→α) for the paraboloid in 𝔽_p^3 holds for all α ≥ 3.

Background

For primes p ≡ 3 mod 4, the paraboloid in 𝔽_p^3 is anisotropic because −1 is not a square. The paper defines R^*(2→α) as the extension estimate from L^2 on this paraboloid to L^α on 𝔽_p^3.

Mockenhaupt and Tao conjectured the sharp threshold α ≥ 3. The paper proves the weaker estimate for α > 10/3, improving earlier bounds, so the conjectured range remains unresolved.