Talk:J-invariant

message: In the beginning of the article j(i)=1728, and in the end j(i)=1. One has something to do with it.  — Preceding unsigned comment added by 95.84.228.116 (talk) 10:41, 22 June 2013 (UTC)
replies: text: I have introduced the alternative notation J=j/1728 at the end of the article to fix this bug in the (somewhat excessive) list of special values. N.Nahber (talk) 21:39, 11 September 2016 (UTC)
thread_title: Notation bugs

message: Elliptic modulus redirects here but is not mentioned.--JohannesBuchner (talk) 14:04, 4 November 2014 (UTC)
replies: text: I have edited the section J-invariant#Alternate_Expressions and clarified that the modular lambda function is the square of the elliptic modulus. Titus III (talk) 00:13, 6 November 2014 (UTC)
thread_title:  Elliptic modulus 

message: The section Special values begins as follows:
"The -invariant vanishes at the "corner" of the fundamental domain at
:\;\;\tfrac{1}{2}\left(1 + i \sqrt{3}\right).
Here are a few more special values (only the first four of which are well known; in what follows,  means  throughout):
BUT: There is no capital-J function defined anywhere in the article.
I see that someone already began a section about notation problems, but that was 2.5 years ago and this problem still persists.
Would someone knowledgeable in this subject please fix this?  E.g., by defining a new function that is j(τ)/1728 instead of using the same notation both for the standard j and a nonstandard j ???
Or else please use the simpler idea of just stating that the list of Special values is a listing of j(τ) /1728 ???Daqu (talk) 19:40, 19 January 2016 (UTC)
replies: text: I have cleaned up this inconsistency by introducing the notation J=j/1728 used by Mathematica N.Nahber (talk) 21:25, 11 September 2016 (UTC)
thread_title:  Nonsensical statement 

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thread_title:  External links modified 

message: The section Special values suddenly seems to use capital J instead of what the rest of the article uses: a lowercase J ("j").
Without any explanation. If the article defines the capital J function somewhere, I haven't found it (and it would not be easy to find).
Can someone knowledgeable on this subject please make this much clearer?50.203.182.230 (talk) 17:37, 31 October 2019 (UTC)
replies: text: As explained towards the beginning of that section, J(\tau)=\frac{1}{1728}\cdot j(\tau). So these are two distinct functions, albeit differing only by a constant (multiplicative) factor. Turgidson (talk) 19:13, 31 October 2019 (UTC)
thread_title:  Why does one section suddenly change the notation? 

message: The section Class field theory and the j-invariant contains this sentence:
"If τ is any CM point, that is, any element of an imaginary quadratic field with positive imaginary part (so that j is defined), then j(τ) is an algebraic integer."
But the meaning of "CM" has not been explained anywhere in the article before this usage.
I hope someone knowledgeable about the subject can fix this bad writing. 2601:200:C000:1A0:3998:89DD:A33:8E64 (talk) 03:31, 25 September 2021 (UTC)
replies: text: CM stands for "complex multiplication" here. This is suggested (not explicitly) later in the section so I added a wikilink there if that can help. TheMathCat 05:45, 25 September 2021 (UTC)
thread_title:  Unexplained terminology 

message: The  first sentence of the section Definition contains the phrase
"with the third definition implying j(𝝉) can be expressed as a cube".
It may be possible for some readers to guess what kind of cube is intended by this statement. 
But since this is an encyclopedia article, it would be much better to state explicitly what kind of "cube" is referred to here. 
Is it "a cube in the field of meromorphic functions on the upper half plane" ?
Of course, the answer is Yes, but I mean: Is this the kind of "cube" referred to in the phrase I quoted? 2601:200:C000:1A0:F4CF:60FC:DCAC:F9C5 (talk) 21:43, 5 June 2022 (UTC)
thread_title:  A cube of what?