Talk:Theta function

From Wikipedia, the free encyclopedia

You have new messages (last change).

[edit] Application

Is there some canonical use for this that I simply can't see? Perhaps in physics or some `simple' math. 19:28, 12 Feb 2005 User:Ub3rm4th

OK, I added a section on the heat equation and also the Heisenberg group. Does that work for you? Its also studied in quantum field theory specifically D-branes and string theory.linas 04:21, 2 Mar 2005 (UTC)

[edit] theta function gives green's function for heat equation ? i dont get the proof.

In Mumford's paper they say theta function gives fundamental solution to the heat equation. To show that i miss the differential operator of the heat equation applied to the theta-function (distribution) for t=0. You say (and Mumford shows) that lim{t->0} theta(x, it) = delta(x) . but what does that help for showing its a fundamental solution?? (unsigned anonymous post 1 jan 2006)

I don't understand the question being asked. Can you rephrase? linas 23:53, 3 January 2006 (UTC)

i think it must be shown: Heat(theta(x, it)){t->0} = delta(x)delta(t) in order to show that theta(x, it) is a fundamental solution, where Heat() shell be the differential operator of the heat equation. (unsigned anonymous post 5 jan 2006)

I still don't understand what you are saying or asking. It is relatively straightforward to to demonstrate that the theta is a solution to the heat equation, and that it satisfies the periodic delta function boundary condition. Are you saying that you are unable to derive this proof on your own? Wikipedia is not the place for long, detailed proofs, which is why this article doesn't have one. If you need help with an equation, you might try asking a question at Wikipedia:Reference desk/Mathematics. linas 23:33, 5 January 2006 (UTC)

[edit] PlanetMath incursions

Someone has made a hash of this article by dumping unedited stuff from PlanetMath in here. Since the notations differ, this was not a good idea. I think I might reedit it to conform, and remove the PlanetMath tags. Gene Ward Smith 22:07, 6 June 2006 (UTC)

I've got the notation consistent now. Gene Ward Smith 05:49, 7 June 2006 (UTC)

Retrieved from "http://en.wikipedia.org../../../t/h/e/Talk%7ETheta_function_fccf.html"