# The current state of Selberg's orthonormality conjecture

I would like to know which results have been obtained concerning Selberg's orthonormality conjecture. For example, has it been proven that for every pair of distinct primitive functions of the Selberg class $(F,G)$, $\displaystyle{\sum_{p\leq x}\frac{a_p(F)\overline{a_p(G)}}{p}=o(\log\log x)}$? Thank you in advance.

EDIT November 5th 2013: considering the answer given below, would the results contained in the following paper: http://arxiv.org/pdf/1311.0754.pdf be a progress toward establishing Selberg's orthonormality conjecture for the whole Selberg class?

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Orthogonality has been proven for certain pairs of automorphic L-functions. The proof procedes like a proof of the Prime Number Theorem, replacing the logarithmic derivative of $\zeta(s)$ with that of $L(s,\pi\otimes\tilde\pi')$, where $\pi$ and $\pi'$ are automorphic representations.
The only proofs in print are for pairs of representations on $GL_m$ (not necessarily the same $m$ for both representations) over ${\mathbb Q}$. It looks like it applies to any pair where the Rankin-Selberg L-function satisfies:
1) Absolutely convergent Euler product for Re(s)$>1$.
4) Nonvanishing for Re(s)$\ge 1$.
5) Order 1 (in the sense that $\log|f(z)|\ll |z|^{1+\epsilon}$), away from the possible pole.