Erdös distance problem in vector spaces over finite fields

• Autores: Alex Iosevich, Misha Rudnev
• Localización: Transactions of the American Mathematical Society, ISSN 0002-9947, Vol. 359, Nº 12, 2007, págs. 6127-6142
• Idioma: inglés
• DOI: 10.1090/s0002-9947-07-04265-1
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• Resumen

  • We study the Erdös/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.