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The paper deals with lower bounds for the remainder term in asymptotics for a certain class of arithmetic functions. Typically, these are generated by a Dirichlet series of the form ζ 2(s)ζ(2s−1)ζ M(2s)H(s), where M is an arbitrary integer and H(s) has an Euler product which converges absolutely for R s > σ0, with some fixed σ0 < 1/2.
Let be the Ramanujan sum, i.e. , where μ is the Möbius function. In a paper of Chan and Kumchev (2012), asymptotic formulas for (k = 1,2) are obtained. As an analogous problem, we evaluate (k = 1,2), where .
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