Talk:Theta function

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)

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)[reply]

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)[reply]

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)[reply]

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

Other notations

How about some mention of, or better yet, a separate article on, the lack of standardization in notation? Abramowitz and Stegun has theta sub four; Whittaker and Watson include a table which shows four other notations not shown here, and some of these define the functions with period pi instead of 1.Cstaffa 02:33, 13 February 2007 (UTC)[reply]

I've thought about this a little bit, Cstaffa, but have not yet reached a conclusion about the best course of action. This article does mention Jacobi's original notation already, although it doesn't say anything about the transformation of variables that leads to period/quasi-period of either (1, τ), or (π, πτ).

Oh – it's not just period π. Two of the functions [the ones involving fractional powers of q, or cos(2n+1)z / sin(2n+1)z] have period 2π, just like the trigonometric functions. But a lot of authors, including Whittaker and Watson, gloss over this point.

I think that A&S implicitly adopted the notation of Tannery & Molk (they refer to W&W, who acknowledge the French guys T&M for the version in Modern Analysis). Anyway, I'm curious … what purpose do you think it would serve to discuss all the different notations for the Theta functions on Wikipedia? Perhaps if we identify a reason why, we can help each other understand the best way to go about it. DavidCBryant 03:09, 13 February 2007 (UTC)[reply]

It would help mopes like me who don't usually deal with such functions who are trying to use formulae pulled from references. I decided to compute g2 for the Weierstrass function with periods 1/2 and 1/2i, so as to get the argument for the parameterization of Costa's minimal surface. I was using A&S and then checked Wikipedia. Not having seen W&W yet, I was confused by the difference in notations. This unsigned comment is from Cstaffa 16:26, 13 February 2007 (UTC)[reply]

Here, don't be too hard on yourself. I had to go look up "Costa's minimal surface" because topology isn't my bag. :-) And I think the various systems of notation are confusing, also. (I don't particularly like the double-subscript notation this article uses, but I didn't write the article – I just stumbled across it and decided it needed some cleanup.)

I can't promise how soon I'll get it done, but I'll put W&W's little table in an article somewhere, and link to that article from this one. Where do you think the link ought to go, Cstaffa? I'm thinking a short italicized sentence at the very beginning to the effect of "See x article for different systems of notation used with Theta functions" would probably work best for someone coming at it from your angle. DavidCBryant 18:29, 13 February 2007 (UTC)[reply]

I think that sounds ideal. I'll have a go at starting it if you don't get to it first.Cstaffa 18:43, 13 February 2007 (UTC)[reply]