On the restriction problem for discrete paraboloid in lower dimension

Misha Rudnev; Ilya D. Shkredov

doi:10.1016/j.aim.2018.10.002

On the restriction problem for discrete paraboloid in lower dimension

Misha Rudnev^*, Ilya D. Shkredov

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

10 Citations (Scopus)

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Abstract

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 language	English
Pages (from-to)	657-671
Number of pages	15
Journal	Advances in Mathematics
Volume	339
Early online date	4 Oct 2018
DOIs	https://doi.org/10.1016/j.aim.2018.10.002
Publication status	Published - 1 Dec 2018

Keywords

Finite fields
Restriction problem

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10.1016/j.aim.2018.10.002

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This is the accepted author manuscript (AAM). The final published version (version of record) is available online via Elsevier at https://doi.org/10.1016/j.aim.2018.10.002 . Please refer to any applicable terms of use of the publisher.
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Cite this

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title = "On the restriction problem for discrete paraboloid in lower dimension",

abstract = "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].",

keywords = "Finite fields, Restriction problem",

author = "Misha Rudnev and Shkredov, {Ilya D.}",

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doi = "10.1016/j.aim.2018.10.002",

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journal = "Advances in Mathematics",

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TY - JOUR

T1 - On the restriction problem for discrete paraboloid in lower dimension

AU - Rudnev, Misha

AU - Shkredov, Ilya D.

PY - 2018/12/1

Y1 - 2018/12/1

N2 - 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].

AB - 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].

KW - Finite fields

KW - Restriction problem

UR - http://www.scopus.com/inward/record.url?scp=85054293098&partnerID=8YFLogxK

UR - https://arxiv.org/abs/1803.11035

U2 - 10.1016/j.aim.2018.10.002

DO - 10.1016/j.aim.2018.10.002

M3 - Article (Academic Journal)

AN - SCOPUS:85054293098

VL - 339

SP - 657

EP - 671

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

ER -

On the restriction problem for discrete paraboloid in lower dimension

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Dr Misha Rudnev

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On the restriction problem for discrete paraboloid in lower dimension

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Dr Misha Rudnev

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