The Finite Field Restriction Problem for the Paraboloid
For the three-dimensional paraboloid over a prime field in which is not a square, the Fourier extension operator maps to for , improving the exponent by combining a bilinear approach with point-line incidence bounds.
- Result
- Proved(see note)
- Status
- Partial result
- AI contribution
- AI-assisted
- Method
- Argument
- Field
- Harmonic analysis
- Posed by
- Gerd Mockenhaupt, Terence Tao
- Year posed
- 2004
- Years open
- 22y
- Solved
- 2026-06-22
- Model
- ChatGPT
- Vendor
- OpenAI
- Collaborators
- Mark Lewko
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 20 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
a record exponent; the conjectured range is not yet reached
What the AI did
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.
Verification
Single-author arXiv preprint; not yet peer-reviewed.
Source
arXiv:2606.22882 - A bilinear approach to the finite field restriction problem, II