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)|
|Number of pages||19|
|State||Published - 2002|
ASJC Scopus subject areas
- Applied Mathematics