75 research outputs found
On linear relations among totally odd multiple zeta values related to period polynomials
We show that there is a relationship between modular forms and totally odd
multiple zeta values, by relating the matrix , whose entries are given
by the polynomial representations of the Ihara action, with even period
polynomials. We also consider the matrix defined by Brown and give a
new upper bound of the rank of . This result gives support to the
uneven part of the motivic Broadhurst-Kreimer conjecture of depth 4.Comment: 34 pages, to appear in Kyushu J. Mat
Relationships between multiple zeta values of depths 2 and 3 and period polynomials
Some combinatorial aspects of relations between multiple zeta values of
depths 2 and 3 and period polynomials are discussed.Comment: I made a major revisio
On Ecalle's and Brown's polar solutions to the double shuffle equations modulo products
Two explicit sets of solutions to the double shuffle equations modulo
products were introduced by Ecalle and Brown respectively. We place the two
solutions into the same algebraic framework and compare them. We find that they
agree up to and including depth four but differ in depth five by an explicit
solution to the linearized double shuffle equations with an exotic pole
structure.Comment: 22 pages, final version, to appear in Kyushu J. Mat
Cyclotomic analogues of finite multiple zeta values
We introduce the notion of finite multiple harmonic q-series at a primitive
root of unity and show that these specialize to the finite multiple zeta value
(FMZV) and the symmetrized multiple zeta value (SMZV) through an algebraic and
analytic operation, respectively. Further, we obtain families of linear
relations among these series which induce linear relations among FMZVs and
SMZVs of the same form. This gives evidence towards a conjecture of Kaneko and
Zagier relating FMZVs and SMZVs. Motivated by the above results, we define
cyclotomic analogues of FMZVs, which conjecturally generate a vector space of
the same dimension as that spanned by the finite multiple harmonic q-series at
a primitive root of unity of sufficiently large degree.Comment: 23 page
Note on totally odd multiple zeta values
A partial answer to a conjecture about the rank of the matrix CN,r introduced by Francis Brown in the study of totally odd multiple zeta values is given
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