An Operator Theoretic Approach to the Prime Number Theorem
(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:
https://lup.lub.lu.se/record/ebb3558a-d5aa-488f-b9dc-e3f82037c474
- author
- Olsen, Jan Fredrik LU
- organization
- publishing date
- 2023
- 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}}, }