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

TL;DR

This paper investigates the distribution of fractional parts of scaled imaginary parts of the zeros of the Riemann zeta function, exploring their connection to pair correlation functions and prime distribution, and extends results to L-functions.

Contribution

It advances understanding of the fractional parts of zeros' imaginary parts and links their distribution to prime number theory and L-functions, building on previous work.

Findings

Connections established between fractional parts and pair correlation functions

Results related to the distribution of primes in short intervals

Extension of results to general L-functions

Abstract

We continue our investigation of the distribution of the fractional parts of $a \gamma$, where $a$ is a fixed non-zero real number and $\gamma$ runs over the imaginary parts of the non-trivial zeros of the Riemann zeta function. We establish some connections to pair correlation functions and the distribution of primes in short intervals. We also discuss analogous results for a more general L-function. This is a sequel to the paper math.NT/0405459.