Survey of Dirichlet Series of Multiplicative Arithmetic Functions

Details Survey of Dirichlet Series of Multiplicative Arithmetic Functions Survey of Dirichlet Series of Multiplicative Arithmetic Functions

2011-06-20

arxiv.org/abs/1106.4038v1

Mathematics

Number Theory

24 pages, no figures

Scientific paper

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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