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

@inproceedings{MurtyExplicitFF,
title={Explicit formulas for the pair correlation of zeros of functions in the Selberg class},
author={Ram Murty and Alexandru Zaharescu}
}

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: P ÿTUgF ; gGUT f rF rG to sums over prime powers, of the form: T p P nV2 LF nLG ng n where f and g are test functions such that f is the Mellin transform of g. As a consequence we ®nd that the Weak Pair Correlation Conjecture for functions in the Selberg class is essentially equivalent to the Selberg Orthonormality Conjectures. 1991 Mathematics Subject Classi… CONTINUE READING