is there a name in use for Dirichlet series without the order term, analogously to Laurent or Puiseux polynomials? Is there work known about such expressions?


$D(s) = \sum\_{0<n<N}a\_n/n^s$


The question came up when implementing Dirichlet series in a computer algebra system.



Dirichlet series without order term
These are called [Dirichlet polynomials](http://www.encyclopediaofmath.org/index.php/Dirichlet_polynomial).


They arise in many places in analytic number theory. For example, in approximate functional equations of $L$-functions.


