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The Finite Field Restriction Problem for the Paraboloid

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finite-field-restriction-paraboloidAnalysisposed by Gerd Mockenhaupt, Terence Tao, 2004recorded: partial

1 attempt · no person has looked

Statement

For the three-dimensional paraboloid P3P_3 over a prime field in which −1-1 is not a square, the Fourier extension operator maps L2L^2 to LrL^r for r>176/51=3.45098…r > 176/51 = 3.45098\ldots, improving the exponent by combining a bilinear approach with point-line incidence bounds.

Context

a record exponent; the conjectured range is not yet reached

The finite field restriction problem, posed by Mockenhaupt and Tao as a model for Euclidean restriction, where the exponent is the standard measure of progress.

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1 attempt

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  • #1

    Attempt 1

    proof attemptChatGPT with Mark Lewko ·
    AI involvement
    ai assisted
    — a person led the work and used a model along the way.
    models
    ChatGPT
    people
    Mark Lewko

    The author states he used ChatGPT to help organize the argument and to identify the cutoffs used to optimize the estimates. Choosing those cutoffs is what fixes the exponent, so the contribution touches the result rather than only the write-up.

    a record exponent; the conjectured range is not yet reached

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