Totally odd depth-graded multiple zeta values and period polynomials

Abstract

Inspired by a paper of Tasaka, we study the relations between totally odd, motivic depth-graded multiple zeta values. Our main objective is to determine the rank of the matrix $C_{N,r}$ defined by Brown. We will give new proofs for (conjecturally optimal) upper bounds on the rank of $C_{N,3}$ and $C_{N,4}$, which were first obtained by Tasaka. Finally, we present a recursive approach to the general problem, which reduces evaluating the rank of $C_{N,r}$ to an isomorphism conjecture.

New version, taking recent developments into account, 14 pages

References in corpus (1)

• On linear relations among totally odd multiple zeta values related to period polynomials

Cited by in corpus (1)

• Depth-graded motivic Lie algebra