Discrete restriction estimates for forms in many variables

Brian Cook; Kevin Hughes; Eyvindur Palsson

doi:10.1017/S0013091523000366

Discrete restriction estimates for forms in many variables

Brian Cook, Kevin Hughes, Eyvindur Palsson

School of Mathematics

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

Abstract

We prove discrete restriction estimates for a broad class of hypersurfaces arising in seminal work of Birch. To do so, we use a variant of Bourgain’s arithmetic version of the Tomas–Stein method and Magyar’s decomposition of the Fourier transform of the indicator function of the integer points on a hypersurface.

Original language	English
Pages (from-to)	923-939
Number of pages	17
Journal	Proceedings of the Edinburgh Mathematical Society
Volume	66
Issue number	4
DOIs	https://doi.org/10.1017/S0013091523000366
Publication status	Published - 1 Nov 2023

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title = "Discrete restriction estimates for forms in many variables",

abstract = "We prove discrete restriction estimates for a broad class of hypersurfaces arising in seminal work of Birch. To do so, we use a variant of Bourgain{\textquoteright}s arithmetic version of the Tomas–Stein method and Magyar{\textquoteright}s decomposition of the Fourier transform of the indicator function of the integer points on a hypersurface.",

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AU - Hughes, Kevin

AU - Palsson, Eyvindur

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N2 - We prove discrete restriction estimates for a broad class of hypersurfaces arising in seminal work of Birch. To do so, we use a variant of Bourgain’s arithmetic version of the Tomas–Stein method and Magyar’s decomposition of the Fourier transform of the indicator function of the integer points on a hypersurface.

AB - We prove discrete restriction estimates for a broad class of hypersurfaces arising in seminal work of Birch. To do so, we use a variant of Bourgain’s arithmetic version of the Tomas–Stein method and Magyar’s decomposition of the Fourier transform of the indicator function of the integer points on a hypersurface.

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DO - 10.1017/S0013091523000366

M3 - Article (Academic Journal)

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VL - 66

SP - 923

EP - 939

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

IS - 4

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Discrete restriction estimates for forms in many variables

Abstract

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