Chebyshev’s bias for Ramanujan’s $\tau$-function via the Deep Riemann Hypothesis

Abstract

The authors assume the Deep Riemann Hypothesis to prove that a weighted sum of Ramanujan's -function has a bias to being positive.This phenomenon is an analogue of Chebyshev's bias.

Locations

• Proceedings of the Japan Academy Series A Mathematical Sciences - View - PDF
• arXiv (Cornell University) - View - PDF