Geodesic
An estimate of Gaussian sums
Matematičeskie zametki, Tome 17 (1975) no. 4, pp. 579-588 
S. B. Stechkin. An estimate of Gaussian sums. Matematičeskie zametki, Tome 17 (1975) no. 4, pp. 579-588. http://geodesic.mathdoc.fr/item/MZM_1975_17_4_a9/
@article{MZM_1975_17_4_a9,
     author = {S. B. Stechkin},
     title = {An estimate of {Gaussian} sums},
     journal = {Matemati\v{c}eskie zametki},
     pages = {579--588},
     year = {1975},
     volume = {17},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_17_4_a9/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Suppose $n\in N$, $n\ge3$, $a\in Z$, $q\in N$, $(a,q)=1$. It is shown that for the Gaussian sums $$ S_n(a,q)=\sum_{k=0}^{q-1}e^{2\pi i\frac aqk^n} $$ the following estimate holds uniformly with respect to all parameters: $$ |S_n(a,q)|\le\exp\{C(n\varphi(n))^2\}q^{1-1/n}, $$ where $C$ is a positive absolute constant and $\varphi(n)$ is Euler's function.