The conservative matrix field

TL;DR

The paper introduces the conservative matrix field, a new mathematical structure that helps analyze properties of famous constants and connects to number theory techniques.

Contribution

It develops the conservative matrix field framework, providing new insights into mathematical constants and their properties, inspired by Apéry's proof techniques.

Findings

Applicable to constants like e, π, ln(2)

Reveals connections to number theory methods

Offers potential for further mathematical investigations

Abstract

We present a new structure called the "conservative matrix field", initially developed to elucidate and provide insight into the methodologies employed by Ap\'ery's in his proof of the irrationality of the Riemann zeta function at 3. This framework is also applicable to other well known mathematical constants, such as e, {\pi}, ln(2), and more, and can be used to study their properties. Moreover, the conservative matrix field exhibits inherent connections to various ideas and techniques in number theory, thereby indicating promising avenues for further applications and investigations.