ON LINEAR RELATIONS AMONG TOTALLY ODD MULTIPLE ZETA VALUES RELATED TO PERIOD POLYNOMIALS

摘要

We show that there is a relationship between modular forms and totally odd multiple zeta values by relating the matrix E-N,E-r, whose entries are given by the polynomial representations of the Ihara action, with even period polynomials. We also consider the matrix C-N,C-r defined by Brown and give a new upper bound of the rank of C-N,C-4. This result gives support to the uneven part of the motivic Broadhurst-Kreimer conjecture of depth 4.