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International Journal of Mathematics and Mathematical Sciences
Volume 2006, Article ID 59482, 5 pages
http://dx.doi.org/10.1155/IJMMS/2006/59482

On the set of distances between two sets over finite fields

Department of Computing, Macquarie University, Sydney, NSW 2109, Australia

Received 13 March 2006; Revised 12 May 2006; Accepted 9 July 2006

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [9 citations]

The following is the list of published articles that have cited the current article.

  • Alex Iosevich, and Doowon Koh, “The Erdös-Falconer distance problem, exponential sums, and fourier analytic approach to incidence theorems in vector spaces over finite fields,” SIAM Journal on Discrete Mathematics, vol. 23, no. 1, pp. 123–135, 2008. View at Publisher · View at Google Scholar
  • Nicholas M. Katz, Igor E. Shparlinski, and Maosheng Xiong, “On character sums with distances on the upper half plane over a finite field,” Finite Fields and Their Applications, vol. 15, no. 6, pp. 738–747, 2009. View at Publisher · View at Google Scholar
  • Le Anh Vinh, “On Sum Of Products And The Erdős Distance Problem Over Finite Fields,” Bulletin of the Australian Mathematical Society, pp. 1–9, 2011. View at Publisher · View at Google Scholar
  • Doowon Koh, and Chun-Yen Shen, “Sharp extension theorems and Falconer distance problems for algebraic curves in two dimensional vector spaces over finite fields,” Revista Matematica Iberoamericana, vol. 28, no. 1, pp. 157–178, 2012. View at Publisher · View at Google Scholar
  • Rainer Dietmann, “On the Erdős–Falconer distance problem for two sets of different size in vector spaces over finite fields,” Monatshefte für Mathematik, vol. 170, no. 3-4, pp. 343–359, 2013. View at Publisher · View at Google Scholar
  • Chun-Yen Shen, and Doowon Kohpp. 411–420, 2014. View at Publisher · View at Google Scholar
  • Doowon Koh, and Hae-Sang Sun, “Distance sets of two subsets of vector spaces over finite fields,” Proceedings of the American Mathematical Society, vol. 143, no. 4, pp. 1679–1692, 2015. View at Publisher · View at Google Scholar
  • David Covert, Doowon Koh, and Youngjin Pi, “ON THE SUMS OF ANY k POINTS IN FINITE FIELDS,” Siam Journal On Discrete Mathematics, vol. 30, no. 1, pp. 367–382, 2016. View at Publisher · View at Google Scholar
  • David Covert, Doowon Koh, and Youngjin Pi, “The Generalized k-Resultant Modulus Set Problem in Finite Fields,” Journal of Fourier Analysis and Applications, 2018. View at Publisher · View at Google Scholar