Abstract
A series of the form
where f is an arithmetical function and s is a real variable, is called a Dirichlet series. It will be called the Dirichlet series of f. There exist Dirichlet series such that for all values of s, the series does not converge absolutely (see Exercise 5.1). If the Dirichlet series of f does converge absolutely for some values of s then for those values of s the series determines a function which, as we shall see, serves as a generating function of f.
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© 1986 Springer-Verlag New York Inc.
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McCarthy, P.J. (1986). Dirichlet Series and Generating Functions. In: Introduction to Arithmetical Functions. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8620-9_5
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DOI: https://doi.org/10.1007/978-1-4613-8620-9_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-96262-7
Online ISBN: 978-1-4613-8620-9
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