Weighted sum formula of multiple $L$-values and its applications

TL;DR

This paper develops algebraic relations for multiple L-values and zeta values of level N, deriving sum and weighted sum formulas, with applications to specific levels 2 and 3.

Contribution

It introduces a new algebraic framework for double shuffle relations of multiple L-values and derives new sum and weighted sum formulas.

Findings

Established algebraic framework for double shuffle relations

Derived sum formulas for multiple L-values of level N

Applied formulas to double zeta values of levels 2 and 3

Abstract

In this paper, we study the multiple $L$-values and the multiple zeta values of level $N$. We set up the algebraic framework for the double shuffle relations of the multiple zeta values of level $N$. Using the regularized double shuffle relations of multiple $L$-values, we give a sum formula and a weighted sum formula of multiple $L$-values. As applications, we give sum formulas and weighted sum formulas of double zeta values of level $2$ and $3$.