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arXiv · 2011.02847

A positivity conjecture related to the Riemann zeta function

Hugues Bellemare·Yves Langlois·Thomas Ransford
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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.

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Hugues Bellemare, Yves Langlois, Thomas Ransford. 2020-11-04. A positivity conjecture related to the Riemann zeta function. https://doi.org/10.1080/00029890.2019.1651165

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