A few conjectures about the multiple zeta values

TL;DR

This paper presents partial solutions to five major conjectures about multiple zeta values, utilizing linear algebra and shuffle products, advancing understanding of their algebraic structure and relation to the Riemann hypothesis.

Contribution

It provides new partial proofs of five conjectures on MZV using linear systems and shuffle products, simplifying previous approaches.

Findings

Partial proofs for five conjectures on MZV

Linear algebra suffices for four of the conjectures

Insights into the algebraic structure of MZV

Abstract

The multiple zeta values (MZV) are a set of real numbers with a beautiful structure as an algebra over the rational numbers. They are related to maybe the most important conjecture on mathematics today, the Riemann hypothesis. In this paper we will show partial solutions to five well known conjectures about the MZV which we partially proved using just linear systems and shuffles products. We saw that to partially solve four of this conjectures we only need linear algebra.