Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593992 | Journal of Number Theory | 2013 | 11 Pages |
Abstract
Let G1,â¦,GnâFp[X1,â¦,Xm] be n polynomials in m variables over the finite field Fp of p elements. A result of Ã. Fouvry and N.M. Katz shows that under some natural condition, for any fixed ε and sufficiently large prime p the vectors of fractional parts({G1(x)p},â¦,{Gn(x)p}),xâÎ, are uniformly distributed in the unit cube [0,1]n for any cube Îâ[0,pâ1]m with the side length h⩾p1/2(logp)1+ε. Here we use this result to show the above vectors remain uniformly distributed, when x runs through a rather general set. We also obtain new results about the distribution of solutions to system of polynomial congruences.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Bryce Kerr, Igor E. Shparlinski,