Ball, Keith M. (2019) Rational approximations to the zeta function. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 475 (2225). 20190033. doi:10.1098/rspa.2019.0033 ISSN 1364-5021.

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Abstract

This article describes a sequence of rational functions which converges locally uniformly to ζ. 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 and by Berry and Keating. However the point here is that the rational approximations look to be susceptible of quantitative estimation.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Functions, Zeta
Journal or Publication Title:	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Publisher:	Royal Society Publishing
ISSN:	1364-5021
Official Date:	1 May 2019
Dates:	Date Event 1 May 2019 Published 1 May 2019 Available 29 March 2019 Accepted
Volume:	475
Number:	2225
Article Number:	20190033
DOI:	10.1098/rspa.2019.0033
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Copyright Holders:	© 2019 The Author(s)
Date of first compliant deposit:	12 April 2019
Date of first compliant Open Access:	12 April 2019
Related URLs:	Publisher

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