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zoorna
#2
Feb27-12, 11:07 AM
P: 3
i'll try to make the question a bit clearer . we have the dirichlet series :

[tex]I(s)= \sum_{n=1}^{\infty}\frac{\alpha(n)}{n^{s}} , \Re(s)>1[/tex]

where [itex]\alpha(n) [/itex] is some arithmetic function of n .

now i am trying to use mellin transform, or any kind of transform akin to that of fourier's, to extract [itex] \alpha(n)[/itex] . i was hoping for a kernel - function of s - that is orthogonal to all terms except for the one containing the integer i want to extract [itex] \alpha(n)[/itex] for . meaning , i am trying to find a function [itex] f(x,s) [/itex] such that :

[tex]
< f(x,s),n^{-s}>=\left\{\begin{matrix}
k & , & x=n & \\
0 & , & o.w &
\end{matrix}\right.
[/tex]

k is a constant

i hope this makes it clearer .