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Abstract: Let be the kth moment of the number of integers coprime to q in an interval of length h centered on its mean . By comparison with the kth centered moment of the binomial distribution with parameters h and P, for which we show uniformly in k, h and P and where is an absolute constant, we prove the following upper bound where is an absolute constant, uniformly in k, h and q provided that every prime factor of q is greater than or equal to h. [Copyright &y& Elsevier]

Suppose that g(n) is an additive real-valued function, W(N) = 4+min λ(λ² + ∑p

Examines the estimate of fractional moments of a trigonometric sum. Binary representation of positive integers; Split of the set of positive integers into two nonintersecting classes; Equation representing the equality; Use of the inequality between the geometric and arithmetic means; Proof of the theorems; Upper bound for the fractional moment of the sum.

Suppose that $g(n)$ is a real-valued additive function and $\backslash tau(n)$ is the number of divisors of $n$. In this paper, we prove that there exists a constant $C$ such that