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Averages in vector spaces over finite fields

Published online by Cambridge University Press:  01 January 2008

ANTHONY CARBERY ,
BRENDAN STONES  and
JAMES WRIGHT
ANTHONY CARBERY
Affiliation:
School of Mathematics and Maxwell Institute of Mathematical Sciences, University of Edinburgh, JCMB, King's Buildings, Mayfield Road, Edinburgh, EH9 3JZ, Scotland. e-mail: A.Carbery@ed.ac.uk
BRENDAN STONES
Affiliation:
The John Henry Newman School, Hitchin Road, Stevenage, Hertfordshire, G1 4AE. e-mail: brendan_maths@postmaster.co.uk
JAMES WRIGHT
Affiliation:
School of Mathematics and Maxwell Institute of Mathematical Sciences, University of Edinburgh, JCMB, King's Buildings, Mayfield Road, Edinburgh, EH9 3JZ, Scotland. e-mail: J.R.Wright@ed.ac.uk
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Abstract

We study the analogues of the problems of averages and maximal averages over a surface in when the euclidean structure is replaced by that of a vector space over a finite field, and obtain optimal results in a number of model cases.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 144 , Issue 1 , January 2008 , pp. 13 - 27
Copyright
Copyright © Cambridge Philosophical Society 2008

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