1. CMB Online first
2. CMB 2010 (vol 53 pp. 654)
3. CMB 2001 (vol 44 pp. 87)
 Lieman, Daniel; Shparlinski, Igor

On a New Exponential Sum
Let $p$ be prime and let $\vartheta\in\Z^*_p$ be of
multiplicative order $t$ modulo $p$. We consider exponential
sums of the form
$$
S(a) = \sum_{x =1}^{t} \exp(2\pi i a \vartheta^{x^2}/p)
$$
and prove that for any $\varepsilon > 0$
$$
\max_{\gcd(a,p) = 1} S(a) = O( t^{5/6 + \varepsilon}p^{1/8}) .
$$
Categories:11L07, 11T23, 11B50, 11K31, 11K38 

4. CMB 1998 (vol 41 pp. 187)
 Loh, W. K. A.

Exponential sums on reduced residue systems
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 $f(x)$.
Category:11L07 
