Restriction and Kakeya phenomena for finite fields

Gerd Mockenhaupt, Terence Tao

Type: Article

Publication Date: 2004-01-15

Citations: 102

DOI: https://doi.org/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.

Locations

Duke Mathematical Journal - View
arXiv (Cornell University) - View - PDF
Duke Mathematical Journal - View
arXiv (Cornell University) - View - PDF

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