Talk:Theta function

message: 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)
replies: text: I agree that Wikipages on mathematical functions should give some discussion on applications. Why were these functions invented or identified in the first place? Also useful to know. With respect to theta functions, for me, I've encountered theta functions when inverse Laplace transforming coth[sqrt[s]]/sqrt[s]. Spanier and Oldham (An Atlas of Functions, 1987, 27:13) note that theta functions often arise in the context of Laplace transforms. So, this might translate into a more general application for problems of impulse response. Sincerely, DoctorTerrella (talk) 17:06, 3 September 2014 (UTC)
thread_title: Application

message: 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)
replies: text: 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)
thread_title:  theta function gives green's function for heat equation ? i dont get the proof. 

message: 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)
thread_title: PlanetMath incursions

message: I don't know anything about theta functions, but this edit might be suspicious.  The identity before the identity is on Mathworld anyways. Akriasas 06:18, 27 February 2007 (UTC)
thread_title:  suspicious edit 

message: In the section on Jacobi identities, it says:
Jacobi's identities describe how theta functions transform under the modular group, which is generated by τ ↦ τ+1 and τ ↦ -1/τ. We already have equations for the first transformation;
However, while it has certainly been mentioned that the theta function is periodic of period 1 in z for \tau fixed, I can't find any mention of the transformation \tau \mapsto \tau + 1.  Am I missing it?
JadeNB (talk) 02:50, 15 May 2008 (UTC)
thread_title:  Transformation under <math>\tau \mapsto \tau + 1</math> 

message: I removed the sentence A theta function is graphed on a polar coordinate system from the introduction.  It seems wrong: at least, any function can be graphed in any coordinate system you like.  It is not amplified in the text.  Deltahedron (talk) 16:51, 9 May 2012 (UTC)
thread_title:  graphed on a polar coordinate system 

message: Wouldn't it be better if the article had the name "Jacobi theta functions"? The article is mentions generalizations in a section, but everything else is about Jacobi theta functions. K9re11 (talk) 22:44, 10 March 2015 (UTC)
thread_title:  The name of the article 

message: It would be nice to elaborate on (or at least include a reference for) that last sentence about line bundles and descent; it is mentioned once and then never again in the article. Michael Lee Baker (talk) 19:25, 6 June 2015 (UTC)
thread_title:  Line bundle 

message: I may be interpreting something wrong here, but the 3D graphs of the four theta functions in this article don't specify whether it's the modulus, the real part or the imaginary part of the theta function that is the z-coordinate in the surface plot.
Isojarv1 (talk) 18:09, 10 July 2019 (UTC)
thread_title:  Graphs of theta functions 

message: Some of the expressions in this article use the cursive theta (ϑ or \vartheta) and others use the regular lowercase theta (θ or \theta). Is the distinction meaningful, like the distinction between ℒ and L and L? If they are different, it would be nice to explain the different meanings, but if they are the same, it would be nice to make the typography consistent to avoid confusing readers just starting to learn the concept. -- Beland (talk) 21:17, 10 August 2023 (UTC)
replies: text: See the section Theta function#Auxiliary functions.  --JBL (talk) 17:46, 11 August 2023 (UTC)
replies: text:  I read through that section, looked at the rest of the article carefully, and I'm still left with questions. I think the pattern is that ϑ(z;τ) and theta with double-number-subscripts are written with the cursive theta, and theta with a single-number-subscript is written with a regular theta? But is that a somewhat random choice made by this article or is it a standard convention? Is the distinction meaningful, or merely stylistic? For example, if I'm hand-writing these equations, do I need to carefully distinguish between cursive and regular theta, or can I just write them all the same? I see that Jacobi theta functions (notational variations) uses cursive theta with single-number-subscript. Is that an error, an arbitrary choice, or a different system of notation? -- Beland (talk) 17:57, 11 August 2023 (UTC)
thread_title:  Character differences in notation 

message: Regarding:
: Die mentioned up directed Delta triangle...
It seems incomprehensible. E.g., is "Die" the German word for "The" ("the")?
--Mortense (talk) 19:44, 2 April 2024 (UTC)
thread_title:  Incomprehensible?