Timeline for multi-index Dirichlet series
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 21, 2009 at 19:57 | comment | added | M.G. | Yes, the analytic side is of great importance here as the main idea is that it is possible to find out about singularities and order of meromorphic continuations of Dirichlet series by studying the convergence of suitable higher-dimensional Dirichlet-series. At least, this seems to be the case for simple and double Dirichlet-series. Thus, some generalization is thinkable. | |
| Nov 20, 2009 at 22:26 | comment | added | Jon Awbrey | Yes, still looking. It's been a while, but my recollection is that adding more variables from the formal power series standpoint was no essential complication, so long as the algebraic side of the manipulations made sense. Are you running into a lot that depends on the analytic side of things? | |
| Nov 20, 2009 at 21:20 | comment | added | M.G. | Actually, combinatorics is not really my field, but I happened to find both volumes of Stanley´s enumerative combinatorics, and from what I have seen, he doesn´t mention multiple Dirichlet series anywhere. I have already looked in Generatingfunctionology, but it seems to discuss only one-dimensional Dirichlet series (and the basics of them). | |
| Nov 17, 2009 at 17:26 | comment | added | Jon Awbrey | Wilf has introductory material in his Generatingfunctionology (2nd ed.), § 2.6, starting from a formal power series standpoint. I'll keep looking for old notes and papers, but I'm guessing all this stuff is nicely tucked away in Maple or Mathematica by now. | |
| Nov 16, 2009 at 22:27 | comment | added | Michael Lugo | If I recall correctly, Stanley doesn't talk about Dirichlet generating functions. He certainly doesn't in Volume 1 of Enumerative Combinatorics; it's possible he does in Volume 2, I suppose, but I don't own Volume 2 so I can't check. | |
| Nov 16, 2009 at 22:22 | history | answered | Jon Awbrey | CC BY-SA 2.5 |