A Dirichlet series is a type of infinite series of the form $$D(s) = \sum_{n=1}^{\infty} \frac{a_n}{n^s}$$, where $a_n$ are complex numbers and $s$ is a complex variable. This series converges in certain regions of the complex plane and is closely related to number theory, particularly in the study of prime numbers and the distribution of arithmetic functions.
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