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Published online by Cambridge University Press: 20 November 2018
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 $f(x)$.