Gould, H. W.; Shonhiwa, Temba A catalog of interesting Dirichlet series. (English) Zbl 1143.11005 Missouri J. Math. Sci. 20, No. 1, 2-18 (2008). Summary: A Dirichlet series is a series of the form\[ F(s)= \sum_{n=1}^\infty \frac{f(n)}{n^s}, \]where the variable \(s\) may be complex or real and \(f(n)\) is a number-theoretic function. The sum of the series, \(F(s)\), is called the generating function of \(f(n)\). The Riemann zeta-function\[ \zeta(s)= \sum_{n=1}^\infty \frac{1}{n^s}= \Pi_p\biggl(1- \frac{1}{p^s}\biggr)^{-1}, \]where \(n\) runs through all integers and \(p\) runs through all primes is the special case where \(f(n)=1\) identically. It is fundamental to the study of prime numbers and many generating functions are combinations of this function. In this paper, we give an overview of some of the commonly known number-theoretic functions together with their corresponding Dirichlet series. Cited in 4 Documents MSC: 11A25 Arithmetic functions; related numbers; inversion formulas 11M41 Other Dirichlet series and zeta functions PDF BibTeX XML Cite \textit{H. W. Gould} and \textit{T. Shonhiwa}, Missouri J. Math. Sci. 20, No. 1, 2--18 (2008; Zbl 1143.11005) OpenURL