Pair correlation of zeros of the real and imaginary parts of the Riemann zeta-function

摘要

We show that if the Riemann Hypothesis is true for the Riemann zeta-function, zeta(s), and 0 alpha 1/2, then all but a finite number of the zeros of R zeta(a, it), I zeta(a + it), and similar functions are simple. We also study the pair correlation of the zeros of these functions assuming the Riemann Hypothesis is true and 0 a = 1/2. (C) 2017 Elsevier Inc. All rights reserved.