## Restriction and Kakeya phenomena for finite fields (2004)

by
Gerd Mockenhaupt
,
Terence Tao

Venue: | DUKE MATH. J |

Citations: | 25 - 0 self |

### BibTeX

@ARTICLE{Mockenhaupt04restrictionand,

author = {Gerd Mockenhaupt and Terence Tao},

title = {Restriction and Kakeya phenomena for finite fields},

journal = {DUKE MATH. J},

year = {2004},

volume = {121},

pages = {35--74}

}

### OpenURL

### 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