Abstract
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(ρF + ρG) to sums over prime powers, of the form: T/πΣn ≥ 2 ΛF(n)ΛG(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.
Original language | English (US) |
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Pages (from-to) | 65-83 |
Number of pages | 19 |
Journal | Forum Mathematicum |
Volume | 14 |
Issue number | 1 |
DOIs | |
State | Published - 2002 |
Externally published | Yes |
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics