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

Abstract

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

34 pages, to appear in Kyushu J. Math

References in corpus (2)

• Zeta elements in depth 3 and the fundamental Lie algebra of a punctured elliptic curve
• The double shuffle relations for multiple Eisenstein series

Cited by in corpus (1)

• Totally odd depth-graded multiple zeta values and period polynomials