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ISSN 1088-6850(e) ISSN 0002-9947(p)

Erdös distance problem in vector spaces over finite fields

Author(s): A. Iosevich; M. Rudnev
Journal: Trans. Amer. Math. Soc. 359 (2007), 6127-6142.
MSC (2000): Primary 11T24, 52C10
Posted: July 20, 2007
MathSciNet review: 2336319
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Abstract: We study the Erdös/Falconer distance problem in vector spaces over finite fields. Let ${\mathbb{F}}_q$ be a finite field with elements and take $E \subset {\mathbb{F}}^d_q$ , $d \ge 2$ . We develop a Fourier analytic machinery, analogous to that developed by Mattila in the continuous case, for the study of distance sets in ${\mathbb{F}}^d_q$ to provide estimates for minimum cardinality of the distance set $\Delta(E)$ in terms of the cardinality of . Bounds for Gauss and Kloosterman sums play an important role in the proof.

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