English

Totally odd depth-graded multiple zeta values and period polynomials

Number Theory 2023-10-13 v2

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 CN,rC_{N,r} defined by Brown. We will give new proofs for (conjecturally optimal) upper bounds on the rank of CN,3C_{N,3} and CN,4C_{N,4}, which were first obtained by Tasaka. Finally, we present a recursive approach to the general problem, which reduces evaluating the rank of CN,rC_{N,r} to an isomorphism conjecture.

Cite

@article{arxiv.1708.07210,
  title  = {Totally odd depth-graded multiple zeta values and period polynomials},
  author = {Charlotte Dietze and Chokri Manai and Christian Nöbel and Ferdinand Wagner},
  journal= {arXiv preprint arXiv:1708.07210},
  year   = {2023}
}

Comments

New version, taking recent developments into account, 14 pages

R2 v1 2026-06-22T21:22:14.977Z