Survey of Dirichlet Series of Multiplicative Arithmetic Functions

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.

Reorganized chapters 3.13 and 3.14. Updated bibliography

References in corpus (5)

• The formal series Witt transform
• Series of Reciprocal Powers of k-almost Primes
• Table of Dirichlet L-Series and Prime Zeta Modulo Functions for Small Moduli
• Hardy-Littlewood Constants Embedded into Infinite Products over All Positive Integers
• On a class of arithmetic convolutions involving arbitrary sets of integers

Cited by in corpus (2)

• Sums involving the number of distinct prime factors function
• On the resummation of series of fuzzy numbers via generalized Dirichlet and generalized factorial series