International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 37853, 5 pages
Distribution of Roots of Polynomial Congruences
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 , we obtain an upper bound on the discrepancy of
fractions , where runs through all of roots modulo of all monic
univariate polynomials of degree whose vector of coefficients belongs
to a -dimensional box . The bound is nontrivial starting with boxes
of size for any fixed and sufficiently large .