On finite multiple zeta values of level two

TL;DR

This paper introduces a level two analogue of finite multiple zeta values, explores their algebraic structure, and presents conjectural bases, parity results, and sum formulas for these values and related sums.

Contribution

It proposes a new level two framework for finite multiple zeta values and conjectural bases, extending the understanding of finite Euler sums.

Findings

Conjectural bases for finite Euler sums and finite multiple zeta values.

Parity results related to level two finite multiple zeta values.

Sum formulas connecting these new elements to existing structures.

Abstract

We introduce and study a ``level two'' analogue of finite multiple zeta values. We give conjectural bases of the space of finite Euler sums as well as that of usual finite multiple zeta values in terms of these newly defined elements. A kind of ``parity result'' and certain sum formulas are also presented.