Sign changes of error terms related to arithmetical functions

d dont l'addition peutetre exprimee comme P n x f(n) = x +P(log(x)) +E(x). Ici P(x) est un polynome, E(x) = P n y(x) b n n x n +o(1) avec (x) = x b xc 1/2. Nous generalisons la methode de Lau et demontrons des resultats sur le nombre de changements de signe pour ces termes d'erreur. Abstract. Let H(x) = P n x (n) n 6 2x. Motivated by a con- jecture of Erdos, Lau developed a new method and proved that #{n T : H(n)H(n + 1) < 0} T. We consider arithmetical functions f(n) = P d|n b d d whose summation can be expressed as P n x f(n) = x +P(log(x))+E(x), where P(x) is a polynomial, E(x) = P n y(x) b n n x n +o(1) and (x) = x b xc 1/2. We generalize Lau's method and prove results about the number of sign changes for these error terms.