Irrationality of the Riemann-Zeta function at the positive integers
Abstract
The Riemann Zeta function, usually denoted by the Greek letter ζ , was defined in 1737 by a Swiss mathematician Leonhard Euler. This function is an infinite converging sum of powers of natural numbers, and it has explicit expressions in terms of π at positive even integers. In this paper we will discuss various irrationality proofs, focusing on irrationality of certain values of the Zeta function.
Fields of Study & Subjects
Advanced Mathematical Identities
Analytic Number Theory Research
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Mathematics Exchange
- Volume
- 17
- Issue
- 1
- Publication date
- 3 March 2026
- Language
- EN