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arXiv · 2006.03934

On summatory arithmetic functions and a Volterra Integral equation

Alexander E Patkowski
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Abstract

We obtain asymptotic results for well known summatory arithmetic functions, such as $\psi(x),$ and establish connections to new summatory functions. A new Volterra integral equation is offered, which is solved by summatory arithmetic functions. We conclude with some further integral formulas and provide number theoretic formulas as applications.

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Alexander E Patkowski. 2020-06-06. On summatory arithmetic functions and a Volterra Integral equation. https://arxiv.org/abs/2006.03934

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