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15 January 2004 Restriction and Kakeya phenomena for finite fields
Gerd Mockenhaupt, Terence Tao
Duke Math. J. 121(1): 35-74 (15 January 2004). DOI: 10.1215/S0012-7094-04-12112-8

Abstract

The restriction and Kakeya problems in Euclidean space have received much attention in the last few decades, and they are related to many problems in harmonic analysis, partial differential equations (PDEs), and number theory. In this paper we initiate the study of these problems on finite fields. In many cases the Euclidean arguments carry over easily to the finite setting (and are, in fact, somewhat cleaner), but there are some new phenomena in the finite case which deserve closer study.

Citation

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Gerd Mockenhaupt. Terence Tao. "Restriction and Kakeya phenomena for finite fields." Duke Math. J. 121 (1) 35 - 74, 15 January 2004. https://doi.org/10.1215/S0012-7094-04-12112-8

Information

Published: 15 January 2004
First available in Project Euclid: 21 December 2003

zbMATH: 1072.42007
MathSciNet: MR2031165
Digital Object Identifier: 10.1215/S0012-7094-04-12112-8

Subjects:
Primary: 42B05
Secondary: 11T24 , 52C17

Rights: Copyright © 2004 Duke University Press

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Vol.121 • No. 1 • 15 January 2004
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