Estimates for Multiplicative Functions on the Set of Shifted Primes

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Abstract

Let ƒi, i = 1, … k, be complex-valued multiplicative functions satisfying the conditions

where αi ε C,

and

(i = 1, …, k), with some 0 < ϱ ≦ 1. Under these conditions we prove that

moreover, if each fi satisfies (*) with C = 0, then there is ϱ1 > 0, such that

holds, where 3 < v < logAx. As a corollary we prove some results about the mean-value of multiplicative functions.

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