hello community.
I need some help
given $k = \sum A_q e^{ia_q s}$ where $k$, and $s$ is known. Can $A_q$ s now be expressed in terms of $a_q$ .
any help in that direction will be appreciated.
hello community. I need some help given $k = \sum A_q e^{ia_q s}$ where $k$, and $s$ is known. Can $A_q$ s now be expressed in terms of $a_q$ . any help in that direction will be appreciated. 

closed as not a real question by Felipe Voloch, fedja, Andres Caicedo, Gerry Myerson, Ryan Budney Dec 5 '11 at 4:23It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center. If this question can be reworded to fit the rules in the help center, please edit the question. 


No, you cannot, at least not at this level of generality. Consider for example $a_q = \frac{\pi}{q}$, $s=1$ and $k=0$. Basically a rootsofunity situation; then each $A_q$ can be a multiple of the proper coefficient of a cyclotomic polynomial. That does 'solve' the problem, in that you get the $A_q$'s in terms of the $a_q$, up to a single free variable. But of course you can also express a finite linear combination of many roots of unity in the same way, thus getting as many free variables as you wish. If the $a_q$ have some structure, then you might be able to say something  thought the problem often reduces to some nasty diophantine equations OR to requiring Schanuel's conjecture to separate things out. Your question is likely to get closed soon unless you make it a lot more precise and motivated. 

