On theq-Analogue of the Pair Correlation Conjecture Original Research Article

Let[formula]where the inner-most sum runs over the imaginary partsγof zeros of DirichletL-functionsL(s,χ) and where[formula]andK(s) is a suitably chosen “kernel.” Under the assumption of the Generalized Riemann Hypothesis we estimate the asymptotic size ofFK(α,Q) asQ→+∞ in the range midαmid<2. This is used to prove that the proportion of simple zeros of all DirichletL-functions is greater than or equal to1112in the sense of the inequality[formula]asQ→+∞.