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The Finite Field Restriction Problem for the Paraboloid

Analysis · posed by Gerd Mockenhaupt, Terence Tao, 2004 · partial

1 comment

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.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    Mark Lewko, using ChatGPT

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai assisted
    — a person led the work and used a model along the way.

    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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Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.