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Completely multiplicative, partial sum ax+O(1)

Source: Miklós Schweitzer 2016, Problem 1

November 2, 2016
Analytic Number Theorynumber theorycomplex numbers

Problem Statement

For which complex numbers α\alpha does there exist a completely multiplicative, complex-valued arithmetic function ff such that ∑n<xf(n)=αx+O(1)  ? \sum_{n<x}f(n)=\alpha x+O(1)\,\,?
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