Negative Sums of Positive Numbers, About Grandi’s Series and a Certain Recurrence of Prime Numbers

5 Pages Posted: 20 Apr 2020

Date Written: March 24, 2020

Abstract

Already in the 18th century, Euler was known to the following account: ∑n = −1/12 (Ramanujan summation). The above infinite sum of natural numbers applies to certain physical issues, including quantum field theory and string theory (e.g. Casimir effect). From a mathematical point of view, it is associated with the so-called Riemann's zeta function. This article derives the above relationship without referring to the Riemann zeta function and the Ramanujan summation method.

Suggested Citation

Berezowski, Marek, Negative Sums of Positive Numbers, About Grandi’s Series and a Certain Recurrence of Prime Numbers (March 24, 2020). Available at SSRN: https://ssrn.com/abstract=3560560 or http://dx.doi.org/10.2139/ssrn.3560560

Marek Berezowski (Contact Author)

Cracow University of Technology ( email )

ul. Warszawska 24
Krakow, 31-155
Poland

HOME PAGE: http://https://www.researchgate.net/profile/Marek_Berezowski

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
34
Abstract Views
183
PlumX Metrics