Good-to-Bad Gram Point Ratio for Riemann Zeta Function

Abstract

In this study, we consider the asymptotic value of the ratio of good-to-bad Gram points for the Riemann zeta function. We present two new results. The first is a relation between the ratio of good-to-bad Gram points and the distribution of Gram intervals that contain a given number of zeros. We relate this to a conjecture of Odlyzko about the locations of the zeros of the Riemann zeta function. The second is the formulation and experimental validation of two symmetry-related conjectures about the location of the zeros.

Keywords:

• Riemann zeta function
• Gram points
• machine learning