Wikipedia:Reference desk/Archives/Mathematics/2010 March 17

= March 17 =

Plank Time
It says

planck time = $$5.39124(27) \times 10^{-44}$$

What is the

$$27$$

?174.3.107.176 (talk) 01:40, 17 March 2010 (UTC)


 * It's the uncertainty. It means (5.39124 +/- 0.00027) *10^-44. The last two digits (the 24) are +/- the two digits in the brackets. 0.00027*10^-44 is the standard error. --01:47, 17 March 2010 (UTC)


 * So 5.39127 *10^-44, ± 0.00024?174.3.107.176 (talk) 03:23, 17 March 2010 (UTC)
 * 5.39124 *10^-44, ± 0.00027*10^-44. HOOTmag (talk) 08:22, 17 March 2010 (UTC)

Local connection between measure preserving transformations
Suppose we have two maps F and G which preserve the Lebesgue measure and such that d(F,G)<ε (say in Ck).

Problem: does it exist a continuous family of maps Ft such that --Pokipsy76 (talk) 19:37, 17 March 2010 (UTC)
 * Ft preserves the Lebesgue measure
 * d(Ft,F)<ε
 * F0=F and F1=G?

Character question
Working on a proof from "Introduction to Elliptic Curves and Modular Forms" by Koblitz. It involves characters and Gauss sums, which I have little experience with and I don't know what's going on. It's Prop 17 on P127 if you happen to have the book. The proof is on P128. There is a limited preview on Google Books but it does not include P128 so the proof is not included.

$$\chi_1$$ is a primitive Dirichlet character modulo N, so a multiplicative character, and $$\xi = e^{2\pi i / N}$$ is an additive character. $$g = \sum_{j=0}^{N-1} \chi_1 (j) \xi^j$$ is the Gauss sum, though I don't know if this is important yet. We define a function $$f_{\chi_1}(z) = \sum_{n=0}^\infty a_n \chi_1(n) q^n$$, where $$q = e^{2\pi i z}$$ and the $$a_n$$ come from a modular form we start out with, $$f(z) = \sum_{n=0}^\infty a_n q^n$$. So, that's just the background and I am stuck on step 1 of the proof. It's probably not very hard. The claim is
 * $$f_{\chi_1}(z) = \sum_{l=0}^{N-1} \chi_1(l) \sum_{n=0}^\infty \left(\frac{1}{N} \sum_{\nu=0}^{N-1} \xi^{(l-n)\nu} \right) a_n q^n$$.

I guess they're just rewriting $$\chi_1(n)$$ in some other form??? I have no idea. Thanks for any help. StatisticsMan (talk) 20:50, 17 March 2010 (UTC)


 * $$\frac{1}{N} \sum_{\nu=0}^{N-1} \xi^{(l-n)\nu}$$ is 0 when l and n are different mod N, and is 1 when they are the same. So that form is just stacking up the terms for each equivalence class mod N. Rckrone (talk) 06:38, 18 March 2010 (UTC)

Lambert W function for a base other than e
y = xn^x

solve for x in terms of y and n?--203.22.23.9 (talk) 21:22, 17 March 2010 (UTC)
 * Never mind, I've figured it out--203.22.23.9 (talk) 21:23, 17 March 2010 (UTC)