An Integral Equation for Riemann’s Zeta Function and Its Approximate Solution

Michael Milgram

Abstract and Applied Analysis, 2020, vol. 2020, issue 1

Abstract: Two identities extracted from the literature are coupled to obtain an integral equation for Riemann’s ξ(s) function and thus ζ(s) indirectly. The equation has a number of simple properties from which useful derivations flow, the most notable of which relates ζ(s) anywhere in the critical strip to its values on a line anywhere else in the complex plane. From this, both an analytic expression for ζ(σ + it), everywhere inside the asymptotic (t⟶∞) critical strip, as well as an approximate solution can be obtained, within the confines of which the Riemann Hypothesis is shown to be true. The approximate solution predicts a simple, but strong correlation between the real and imaginary components of ζ(σ + it) for different values of σ and equal values of t; this is illustrated in a number of figures.

Date: 2020
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2020/1832982

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2020:y:2020:i:1:n:1832982

Access Statistics for this article

More articles in Abstract and Applied Analysis from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().