Sur la répartition des entiers premiers à un entier sans petit facteur premier

Let Mk(q;h) be the kth moment of the number of integers coprime to q in an interval of length h centered on its mean hφ(q)q. By comparison with the kth centered moment of the binomial distribution with parameters h and P, for which we showμk(h,P)≪(ck)k/2(k+hP(1−P))k/2, uniformly in k, h and P and where c>0 is an absolute constant, we prove the following upper boundMk(q;h)≪(c′k)k/2q(k+hφ(q)q)k/2, where c′>0 is an absolute constant, uniformly in k, h and q provided that every prime factor of q is greater than or equal to h.