11. Formal Dirichlet series are often classified as generating functions, although they are not strictly formal power series. 12. Hence the coefficients of the product of two Dirichlet series are the multiplicative convolutions of the original coefficients. 13. The eta function is defined by an alternating Dirichlet series , so this method parallels the earlier heuristics. 14. There are many applications of this kind of result in number theory, in particular in handling Dirichlet series . 15. His results on power and Dirichlet series , and coauthored a book on the latter with G . H . Hardy. 16. A Dirichlet series may converge absolutely for all, for no or for some values of " s ". 17. In many cases, a Dirichlet series can be extended to an analytic function outside the domain of convergence by analytic continuation. 18. The most usually seen definition of the Riemann zeta function is a Dirichlet series , as are the Dirichlet L-functions. 19. The Dirichlet series case is more complicated, though : absolute convergence and uniform convergence may occur in distinct half-planes. 20. Thus, there might be a strip between the line of convergence and absolute convergence where a Dirichlet series is conditionally convergent.
