##  [Dirichlet Series](/dirichlet-series) 

  ##  [Dirichlet Series](https://puremath.quantumdictionary.io/dirichlet-series-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A Dirichlet series is a complex series of the form Σ_{n≥1} a_n n^{-s}, where s is a complex variable and (a_n) is a sequence of complex coefficients; it serves as a generating function for arithmetic sequences and is central in analytic number theory.