Timeline for Is there a probabilistic interpretation of Dedekind zeta functions?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 29, 2011 at 3:19 | comment | added | user5831 | This might be relevant: arxiv.org/pdf/1106.5618 | |
| Jun 13, 2011 at 14:39 | comment | added | user5831 | Thank you very much for the nice reference! I agree about the positivity issue, this is why I was asking for Dedekind zeta functions. There my feeling is that there might be a nice probabilistic interpretation, for L-functions involving a character it is much less clear what one should do (if possible at all). | |
| Jun 12, 2011 at 22:06 | comment | added | Simon Lyons | I think there may be issues related to positivity of the generalised theta functions. Biane, Pitman and Yor encountered a similar problem when they considered more general L functions. See section six of this paper: citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.160.3091 | |
| Jun 12, 2011 at 14:36 | history | edited | user5831 | CC BY-SA 3.0 |
added 500 characters in body; edited tags
|
| Jun 12, 2011 at 14:31 | comment | added | user5831 | Dear Simon, is it possible to argue that these distributions may arise from a random walk on an appropriate space? The distribution mentioned above is related to the classical theta function and for general number fields we know by the work of Hecke how to write down "generalized theta functions" whose Mellin transform give rise to completed Dedekind zeta functions. In some sense I am asking if the work of Hecke has a probabilistic interpretation? | |
| Jun 11, 2011 at 17:32 | comment | added | Simon Lyons | You can certainly construct analogues of the zeta distribution that take values in other number fields by means of a Dedekind zeta function. These have similar properties to the standard zeta distribution, including the "independence of prime factors" property. | |
| Jun 11, 2011 at 15:07 | comment | added | user5831 | Dear George, thank you very much for the clarification! | |
| Jun 11, 2011 at 14:01 | comment | added | George Lowther | The limiting measure is just the distribution of the maximum of a Brownian motion. I also did this calculation in a recent answer on math.stackexchange. math.stackexchange.com/questions/38642/…. I'm not aware of links with other types of zeta functions though. | |
| Jun 11, 2011 at 13:36 | history | asked | user5831 | CC BY-SA 3.0 |