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 P: 3 i'll try to make the question a bit clearer . we have the dirichlet series : $$I(s)= \sum_{n=1}^{\infty}\frac{\alpha(n)}{n^{s}} , \Re(s)>1$$ where $\alpha(n)$ 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 $\alpha(n)$ . 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 $\alpha(n)$ for . meaning , i am trying to find a function $f(x,s)$ such that : $$< f(x,s),n^{-s}>=\left\{\begin{matrix} k & , & x=n & \\ 0 & , & o.w & \end{matrix}\right.$$ k is a constant i hope this makes it clearer .