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arXiv · 1303.5617

On the asymptotic density of the support of a Dirichlet convolution

Carlo Sanna
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Abstract

Let v be a multiplicative arithmetic function with support of positive asymptotic density. We prove that for any not identically zero arithmetic function f such that \sum_{f(n) \neq 0} 1 / n < \infty, the support of the Dirichlet convolution f * v possesses a positive asymptotic density. When f is a multiplicative function, we give also a quantitative version of this claim. This generalizes a previous result of P. Pollack and the author, concerning the support of Möbius and Dirichlet transforms of arithmetic functions.

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Carlo Sanna. 2013-03-22. On the asymptotic density of the support of a Dirichlet convolution. https://doi.org/10.1016/j.jnt.2013.07.012

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