On transcendental numbers: new results and a little history

TL;DR

This paper surveys transcendental numbers, explores properties of e and pi, introduces new inequalities and identities, discusses implications for Yang-Baxter equations, and proposes open problems in the field.

Contribution

It provides a unified framework for studying transcendental numbers, presents new inequalities and identities, and connects these results to the Yang-Baxter equations.

Findings

New inequalities for transcendental numbers

Identities involving e and pi

Implications for Yang-Baxter equations

Abstract

Attempting to create a general framework for studying new results on transcendental numbers, this paper begins with a survey on transcendental numbers and transcendence, it then presents several properties of the transcendental numbers $e$ and $\pi$, and then it gives the proofs of new inequalities and identities for transcendental numbers. Also, in relationship with these topics, we study some implications for the theory of the Yang-Baxter equations, and we propose some open problems.