Talk:J-invariant

Notation bugs

There is a notational problem in this and related articles; standard notation seems to be that $J=g_2^3/\Delta$ and j=1728 J. I'll try to review correctness/fix this when I have the chance. (where $g_2=60 \sum(m\tau+n)^{-4}$ linas 03:54, 20 Jun 2005 (UTC)

If It can be of any help I think I remember there are two notations for Eisenstein series too: $g_2$ or $G_2$, correspoing to different conventions (leading coefficient one, integer coefficients, norm 1 etc...)

Why is the elliptic modular function attributed to Klein? The fundamental domain of the modular group was known to Gauss. It was studied by Kummer, and by Hermite (1858) in connection with the solution of 5-ics, and defined by Dedekind in a remarkable paper in Crelle ?1878. Klein became involved after Dedekind. He defined j in terms of absolute invariants of Int dx/y, y^2 = 4-ic in x. After a fw pages he reverts to Dedekind's definition. [John McKay] May be Atkin should be consulted?]

Confusing article

"the Fourier coefficients for the positive exponents of q are the dimensions of the grade-n part" - It's not clear what n is. Does it mean the coefficient corresponding to q^n in the q-expansion?

"the rate of growth of ln(cn) is" - cn is never defined in the article. Does it mean the coefficient corresponding to q^n? Also, the asymptotic formula shows the growth of ln(cn), not its rate of growth.

"there are exactly 6486 of them [functions]... (see here for the complete list)" - The link is to a document which appears to not define a single function. For example, "14A0 14B 28B 1 1 1 2C0 71B0 14" does not seem to be a function. —Preceding unsigned comment added by 209.67.107.10 (talk • contribs) 17:54, 6 July 2009

The three quotations were added respectively by User:Nbarth (20 October 2007), by User:Gene Ward Smith (24 May 2006), and by User:R.e.b. (14 May 2006). I have drawn the attention of these three editors to the above comment. However, Gene Ward Smith has not edited since 24 December 2008, so a response is perhaps unlikely. JamesBWatson (talk) 11:48, 10 December 2009 (UTC)

Hi James – thanks for drawing my attention to this.

Anon (209.67.107.10) is correct, the grade-n dimension corresponds to the coefficient of $q^n.$ I’ve clarified this, and included a link to the Griess algebra as the first example.

—Nils von Barth (nbarth) (talk) 19:37, 10 December 2009 (UTC)

I have removed the doubtful material in the other two cases: if anyone can restore and clarify them please do so. JamesBWatson (talk) 10:33, 14 December 2009 (UTC)