International Association
for Cryptologic Research

Consider a collection $f$ of polynomials $f_i(x)$, $i=1, \\ldots,s$, with integer coefficients such that polynomials $f_i(x)-f_i(0)$, $i=1, \\ldots,s$, are linearly independent. Denote by $D_m$ the discrepancy for the set of points $\\left(\\frac{f_1(x) \\bmod m}{m},\\ldots,\\frac{f_s(x) \\bmod m}{p^n}\\right)$ for all $x \\in \\{0,1,\\ldots,m\\}$, where $m=p^n$, $n \\in N$, and $p$ is a prime number. We prove that $D_m\\to 0$ as $n\\to\\infty$, and $D_m