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We study the Erdös/Falconer distance problem in vector spaces over finite fields. Let Fq be a finite field with q elements and take E ⊂ Fdq, d ≥ 2. We develop a Fourier analytic machinery, analogous to that developed by Mattila in the continuous case, for the study of distance sets in Fdq to provide estimates for minimum cardinality of the distance set ∆(E) in terms of the cardinality of E. Bounds for Gauss and Kloosterman sums play a