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arXiv · 1106.4038

Survey of Dirichlet Series of Multiplicative Arithmetic Functions

Richard J. Mathar
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Abstract

The manuscript reviews Dirichlet Series of important multiplicative arithmetic functions. The aim is to represent these as products and ratios of Riemann zeta-functions, or, if that concise format is not found, to provide the leading factors of the infinite product over zeta-functions. If rooted at the Dirichlet series for powers, for sums-of-divisors and for Euler's totient, the inheritance of multiplicativity through Dirichlet convolution or ordinary multiplication of pairs of arithmetic functions generates most of the results.

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Richard J. Mathar. 2012-07-04. Survey of Dirichlet Series of Multiplicative Arithmetic Functions. https://arxiv.org/abs/1106.4038

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