International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 37853, 5 pages
Research Article

Distribution of Roots of Polynomial Congruences

Igor E. Shparlinski

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

Received 7 March 2007; Accepted 7 June 2007

Academic Editor: George E. Andrews

Copyright © 2007 Igor E. Shparlinski. 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.


For a prime p, we obtain an upper bound on the discrepancy of fractions r/p, where r runs through all of roots modulo p of all monic univariate polynomials of degree d whose vector of coefficients belongs to a d-dimensional box . The bound is nontrivial starting with boxes of size ||pd/2+ɛ for any fixed ɛ<0 and sufficiently large p.