# nt.quantity concept – What is thought about absolute convergence of Dirichlet inverses? Answer

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nt.quantity concept – What is thought about absolute convergence of Dirichlet inverses?

Given an arithmetic duty $$f$$ such that the partial sums $$sum_{n leq x} |f(n)|$$ converge as $$x$$ approaches $$infty$$, are there any outcomes regarding the convergence properties of the succession of sums of the figure $$sum_{n leq x} |f^{-1}(n)|$$, the place $$f^{-1}$$ is the Dirichlet inverse of $$f$$? Are there particular, identified circumstances below which these sums will converge as nicely?

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