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# Exponential sums on reduced residue systems

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Published:1998-06-01
Printed: Jun 1998
• W. K. A. Loh
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## Abstract

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 $f(x)$.
 MSC Classifications: 11L07 - Estimates on exponential sums

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