| 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.
|
