Talk:Dedekind eta function
Page contents not supported in other languages.
Systems Mid‑importance | ||||||||||
|
Why is this article in the "fractals" category? —Preceding unsigned comment added by 94.170.104.35 (talk) 22:58, 15 July 2009 (UTC)[reply]
The general modular transformation gives the eta function an argument z on the r.h.s., \tau would be more readable. (anon poster Dec 2005)
\epsilon(a,b,c,d) seems to be independent of b, is this right? (anon poster Dec 2005)
The text mentions that eta is a modular function of weight 1/2. It'd be useful to include its level, and possibly character as well.
I think the definition of eta shown here was wrong and instead of q^(1/24) it should be exp(i pi tau / 12) as I've made it. If the latter expression was implied in the first place, then that should be mentioned since the two expressions are ordinarily different.
The former expression, q^(1/24) led to some problems:1. Take tau=1/2 + i * sqrt(3)/2. Then -1/tau = -1/2 + i * sqrt(3/2) = tau - 1.Note that q corresponding to that tau is -exp(-pi*sqrt(3)), while the q corresponding to -1/tau = tau - 1 is the exact same value.Thus the Dedekind eta function has the same value at both tau and -1/tau.But then the functional equation says that eta(-1/tau) = sqrt(-i*tau) * eta(tau), i.e. 1 = sqrt(-i*tau). This is incorrect.1 is not the square root of (-i/2 + sqrt(3)/2).
2.Another problem is when tau = -1/2 + 0.01i, then eta(tau+1) = eta(tau) and the exp(i pi/12) factor couldn't be correct.Doubledork (talk) 23:02, 13 January 2012 (UTC)[reply]