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An Operator Theoretic Approach to the Prime Number Theorem

Olsen, Jan Fredrik LU (2023) In Journal of Mathematical Physics, Analysis, Geometry 19(1). p.172-177
Abstract

We establish an operator theoretic version of the Wiener–Ikehara Taube-rian theorem and use it to obtain a short proof of the Prime number theorem that should be accessible to anyone with a basic knowledge of operator theory and Fourier analysis.

Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
integral operators, prime number theorem, Tauberian theorems
in
Journal of Mathematical Physics, Analysis, Geometry
volume
19
issue
1
pages
6 pages
publisher
ILTPE-B. Verkin Institute for Low Temperature Physics and Engineering
external identifiers
  • scopus:85159227797
ISSN
1812-9471
DOI
10.15407/mag19.01.172
language
English
LU publication?
yes
id
ebb3558a-d5aa-488f-b9dc-e3f82037c474
date added to LUP
2023-08-15 09:25:02
date last changed
2023-08-15 09:25:02
@article{ebb3558a-d5aa-488f-b9dc-e3f82037c474,
  abstract     = {{<p>We establish an operator theoretic version of the Wiener–Ikehara Taube-rian theorem and use it to obtain a short proof of the Prime number theorem that should be accessible to anyone with a basic knowledge of operator theory and Fourier analysis.</p>}},
  author       = {{Olsen, Jan Fredrik}},
  issn         = {{1812-9471}},
  keywords     = {{integral operators; prime number theorem; Tauberian theorems}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{172--177}},
  publisher    = {{ILTPE-B. Verkin Institute for Low Temperature Physics and Engineering}},
  series       = {{Journal of Mathematical Physics, Analysis, Geometry}},
  title        = {{An Operator Theoretic Approach to the Prime Number Theorem}},
  url          = {{http://dx.doi.org/10.15407/mag19.01.172}},
  doi          = {{10.15407/mag19.01.172}},
  volume       = {{19}},
  year         = {{2023}},
}