On the restriction problem for discrete paraboloid in lower dimension

Misha Rudnev*, Ilya D. Shkredov

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

14 Citations (Scopus)
150 Downloads (Pure)


We apply geometric incidence estimates in positive characteristic to prove the optimal L2→L3 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 L2→L[Formula presented] extension estimate, improving the previously known exponent [Formula presented].

Original languageEnglish
Pages (from-to)657-671
Number of pages15
JournalAdvances in Mathematics
Early online date4 Oct 2018
Publication statusPublished - 1 Dec 2018


  • Finite fields
  • Restriction problem


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