A positivity conjecture related to the Riemann zeta function
Number Theory
2020-11-06 v1 Complex Variables
Abstract
According to two remarkable theorems of Nyman and B\'aez-Duarte, the Riemann hypothesis is equivalent to a simply-stated criterion concerning least-squares approximation. In carrying out computations related to this criterion, we have observed a curious phenomenon: for no apparent reason, at least the first billion entries of a certain infinite triangular matrix associated to the Riemann zeta function are all positive. In this article we describe the background leading to this observation, and make a conjecture.
Cite
@article{arxiv.2011.02847,
title = {A positivity conjecture related to the Riemann zeta function},
author = {Hugues Bellemare and Yves Langlois and Thomas Ransford},
journal= {arXiv preprint arXiv:2011.02847},
year = {2020}
}