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 …n†LG…n†g…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

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