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

  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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Showing 1-10 of 14 references

The Pair Correlation of Zeros of Functions in the Selberg Class

M. R. Murty, A. Perelli
IMRN • 1999
View 9 Excerpts
Highly Influenced

Old and new conjectures and results about a class of Dirichlet series

A. Selberg
Proceedings of the Amal® Conference on Analytic Number Theory (Maiori, • 1989
View 3 Excerpts
Highly Influenced

On the non-vanishing of a certain class of Dirichlet series

S. Narayanan
Canad. Math. Bull. Vol • 1997
View 2 Excerpts

Stronger multiplicity one for Selberg's class. In: Harmonic analysis and Number theory (ed

M. R. Murty
CMS Conf. Proceedings Vol • 1997
View 1 Excerpt

Principal L - functions and Random Matrix Theory ,

Z. Rudnick, P. Sarnak
Duke Math . J . • 1996

Principal L-functions and Random Matrix

Z. Rudnick, P. Sarnak
Theory, Duke Math. J., 81, • 1996
View 3 Excerpts

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