Exponential sums on reduced residue systems

http://dx.doi.org/10.4153/CMB-1998-028-5
Canad. Math. Bull. 41(1998), 187-195

  Published:1998-06-01
 Printed: Jun 1998

The aim of this article is to obtain an upper bound for the exponential sums $\sum e(f(x)/q)$, where the summation runs from $x=1$ to $x=q$ with $(x,q)=1$ and $e(\alpha)$ denotes $\exp(2\pi i\alpha)$. We shall show that the upper bound depends only on the values of $q$ and $s$, %% where $s$ is the number of terms in the polynomial $f(x)$.