Pls proove this

$\displaystyle y(p,q)=\lim_{N \to \infty}\frac{1}{N} \sum^{N-1}_{l=0} e^{i(pl+ql^{2})}=0 $

for p≠0, 2π, 4π, ... and q≠0, 2π, 4π, ...

~Kalyan.

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- Jun 22nd 2008, 11:37 PMkalyanramProove this identity
Pls proove this

$\displaystyle y(p,q)=\lim_{N \to \infty}\frac{1}{N} \sum^{N-1}_{l=0} e^{i(pl+ql^{2})}=0 $

for p≠0, 2π, 4π, ... and q≠0, 2π, 4π, ...

~Kalyan. - Jun 23rd 2008, 05:02 AMCaptainBlack
All you are going to get from this approach is that the limit is less than or equal to $\displaystyle 1$.

A hand-waving argument would go that the complex exponentials are of unit magitude and random phase so as $\displaystyle N$ becomes large the sum goes as $\displaystyle \sqrt{N}$ , but we divide by $\displaystyle N$ so $\displaystyle y$ goes to $\displaystyle 0$.

Unfortunatly I see no way to make this rigourous so some more thought is needed.

RonL - Jun 23rd 2008, 08:37 AMOpalg