Abstract
Abstract
In studying the depth filtration on multiple zeta values, difficulties quickly arise due to a disparity between it and the coradical filtration [9]. In particular, there are additional relations in the depth graded algebra coming from period polynomials of cusp forms for
$\operatorname {\mathrm {SL}}_2({\mathbb {Z}})$
. In contrast, a simple combinatorial filtration, the block filtration [13, 28] is known to agree with the coradical filtration, and so there is no similar defect in the associated graded. However, via an explicit evaluation of
$\zeta (2,\ldots ,2,4,2,\ldots ,2)$
as a polynomial in double zeta values, we derive these period polynomial relations as a consequence of an intrinsic symmetry of block graded multiple zeta values in block degree 2. In deriving this evaluation, we find a Galois descent of certain alternating double zeta values to classical double zeta values, which we then apply to give an evaluation of the multiple t values [22]
$t(2\ell ,2k)$
in terms of classical double zeta values.
Publisher
Cambridge University Press (CUP)
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