Survey of Dirichlet Series of Multiplicative Arithmetic Functions
Number Theory
2012-07-05 v2
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.
Keywords
Cite
@article{arxiv.1106.4038,
title = {Survey of Dirichlet Series of Multiplicative Arithmetic Functions},
author = {Richard J. Mathar},
journal= {arXiv preprint arXiv:1106.4038},
year = {2012}
}
Comments
Reorganized chapters 3.13 and 3.14. Updated bibliography