Abstract :
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 image. By comparison with the kth centered moment of the binomial distribution with parameters h and P, for which we showμk(h,P)much less-than(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 boundimage 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.
