Une remarque sur les sommes de Ramanujan

We study the asymptotic behaviour of the function $A(q)={\sup }_{x,y}|{\sum }_{x<n?y}{c}_q(n)|$ where $c_q(n)$ denotes the Ramanujan sum. We prove that $q?A(q)?q\sqrt{{\log }_{2}q}$ and determine how sharp this estimation is. To cite this article: A. Chadozeau, C. R. Acad. Sci. Paris, Ser. I 341 (2005).