Year: 2017
Type: preprint
Abstract: This article describes a sequence of rational functions which converges locally uniformly to the zeta function. The numerators (and denominators) of these rational functions can be expressed as characteristic polynomials of matrices that are on the face of it very simple. As a consequence, the Riemann hypothesis can be restated as what looks like a rather conventional spectral problem but which is related to the one found by Connes in his analysis of the zeta function. However the point here is that the rational approximations look to be susceptible of quantitative estimation.
Source: arXiv (Cornell University)
Author: Ball, Keith
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4299365135