Discrete restriction estimates of epsilon-removal type for kth-powers\n and k-paraboloids

2016/10/13 by Kevin Henriot, Henriot, Kevin, Kevin Hughes +2 · 1 citation
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Nonlinear Partial Differential Equations #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1610.03984

openalex publication_date 2016/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain restriction estimates of \ε-removal type for the set of\nk-th powers of integers, and for discrete d-dimensional surfaces of the\nform \
(n₁,
dots,n_d,n₁^k +
dotsb + n_d^k)
,:
, |n₁|,
dots,|n_d|
leq\nN
, which we term 'k-paraboloids'. For these surfaces, we obtain a\nsatisfying range of exponents for large values of d,k. We also obtain\nestimates of \ε-removal type in the full supercritical range for k-th\npowers and for k-paraboloids of dimension d < k(k-2). We rely on a variety\nof techniques in discrete harmonic analysis originating in Bourgain's works on\nthe restriction theory of the squares and the discrete parabola.\n

Citations

• On Λ(p)-subsets of squares

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• Discrete restriction for (x,x³) and related topics

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