On the distribution of imaginary parts of zeros of the Riemann zeta function,II

We continue our investigation of the distribution of the fractional parts of αγ, where α is a fixed non-zero real number and γ runs over the imaginary parts of the non-trivial zeros of the Riemann zeta function. We establish some connections to Montgomery’s pair correlation function and the distribution of primes in short intervals. We also discuss analogous results for a more general L-function. The first author is supported by National Science Foundation Grant DMS-0555367. The second author is partially supported by the National Science Foundation and the American Institute of Mathematics (AIM). The third author is supported by National Science Foundation Grant DMS-0456615.