Explicit formulas for the pair correlation of zeros of functions in the Selberg class

For any two functions F and G in the Selberg class we prove explicit formulas which relate sums over pairs of zeros, of the form: Σ_{-T ≤ γF, γG ≤ T} f(ρ_F + ρ_G) to sums over prime powers, of the form: T/πΣ_{n ≥ 2} Λ_F(n)Λ_G(n)g(n) where f and g are test functions such that f is the Mellin transform of g. As a consequence we find that the Weak Pair Correlation Conjecture for functions in the Selberg class is essentially equivalent to the Selberg Orthonormality Conjectures.