Bounded Additive Relation and Application to Finite Multiple Zeta Values

TL;DR

This paper introduces a new algebraic approach to identify linear relations among finite multiple zeta values using bounded coefficients, employing the MITM algorithm and Chinese remainder theorem to generate a comprehensive relation table.

Contribution

It formulates an algebraic problem for bounded coefficient relations in Abelian groups and applies the MITM algorithm to finite multiple zeta values, providing new computational insights.

Findings

Generated a table of expected linear relations for finite multiple zeta values of weight 10.

Demonstrated the effectiveness of the MITM algorithm combined with Chinese remainder theorem in this context.

Established a new algebraic framework for analyzing relations in finite Abelian groups.

Abstract

We formulate an algebraic problem to find a generating system of a finite subset of an Abelian group with respect to linear relations whose coefficients are bounded by a constant, and recall MITM algorithm for the problem. As an application of MITM algorithm for the Abelian group \begin{eqnarray*} \mathbb{Z}/106700590455862347842907841856033238416352421 \mathbb{Z} \end{eqnarray*} combined with Chinese remainder algorithm, we give a table of expected linear relations of finite multiple zeta values of weight $10$.