Erdös distance problem in vector spaces over finite fields
By Alex Iosevich, M. Rudnev. 2005
222 citations recorded by the source corpus.
We study the Erdos/Falconer distance problem in vector spaces over finite fields. Let be a finite field with elements and take , . We develop a Fourier analytic machinery, analogous to that developed by Mattila in the continuous case, for the study of distance sets in to provide estimates for minimum cardinality of the distance set in terms of the cardinality of . Bounds for Gauss and Kloosterman sums play an important role in the proof.
Subfields: Algebra and Number Theory, Artificial Intelligence, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/8af4990785f8c0a37084b40f3e7d193f02f16e56
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In Algebra and Number Theory
In Artificial Intelligence
In Discrete Mathematics and Combinatorics
Citations in the corpus
- Averages over hyperplanes, sum-product theory in vector spaces over finite fields and the Erdos-Falconer distance conjecture (2007, methodology): “In view of the examples cited in the previous paragraph, Iosevich and Rudnev ([12]) formulated the Erdős-Falconer conjecture as follows.”
- Sums and products in finite fields: an integral geometric viewpoint (2007, unknown): “and in [9] the underlying operator is Atf(x) = ∑ y2 1+···+y d=t f(x− y),”
- Pinned distance sets, k-simplices, Wolff’s exponent in finite fields and sum-product estimates (2009, background): “In [20] the following result is given that gives us a lower bound on the size of the distance set in terms of the upper bound on ME(q).”