Extension theorems for paraboloids in the finite field setting

DOI10.1007/S00209-009-0580-1zbMath1203.42013arXiv0805.0814OpenAlexW2051615888MaRDI QIDQ5962181

Alexander Iosevich, Doowon Koh

Publication date: 21 September 2010

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0805.0814

zbMATH Keywords

Gauss sumfinite fielddiscrete Fourier transformextension operator

Mathematics Subject Classification ID

Other character sums and Gauss sums (11T24) Fourier series and coefficients in several variables (42B05)

Related Items (13)

Endpoint restriction estimates for the paraboloid over finite fields ⋮ Averaging operators over homogeneous varieties over finite fields ⋮ New restriction estimates for the 3-d paraboloid over finite fields ⋮ Sharp extension theorems and Falconer distance problems for algebraic curves in two dimensional vector spaces over finite fields ⋮ Extension theorems for Hamming varieties over finite fields ⋮ Weak version of restriction estimates for spheres and paraboloids in finite fields ⋮ On the Sums of Any $k$ Points in Finite Fields ⋮ Finite field restriction estimates based on Kakeya maximal operator estimates ⋮ Conjecture and improved extension theorems for paraboloids in the finite field setting ⋮ Extension theorems and a connection to the Erdős-Falconer distance problem over finite fields ⋮ Finite field analogue of restriction theorem for general measures ⋮ Finite field restriction estimates for the paraboloid in high even dimensions ⋮ Restriction estimates for the flat disks over finite fields

Cites Work

• Extension theorems for the Fourier transform associated with nondegenerate quadratic surfaces in vector spaces over finite fields
• Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
• Some sharp restriction theorems for homogeneous manifolds
• Restriction and Kakeya phenomena for finite fields
• The Bochner-Riesz conjecture implies the restriction conjecture
• Inequalities for strongly singular convolution operators
• Extension theorems for spheres in the finite field setting
• On Fourier coefficients and transforms of functions of two variables
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