On summatory arithmetic functions and a Volterra Integral equation

2020/06/06 by Patkowski, Alexander E
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2006.03934

Abstract

We obtain asymptotic results for well known summatory arithmetic functions, such as ψ(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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