### Honorary MZVs and modular forms

Broadhurst, DJ *(Open University)*

Monday 08 April 2013, 11:00-12:00

Seminar Room 1, Newton Institute

#### Abstract

$\sum_{a>b>c>d>e>0}(-1)^{b+d}/(a^3b^6c^3d^6e^3)$ is an alternating sum with weight 21 and depth 5, yet has a conjectural expression as a Q-linear combination of multiple zeta values (MZVs) that includes a sum of depth 7. The MZV Data Mine [arXiv:0907.2557] contains many other examples of "honorary MZVs", i.e. alternating sums that are reducible to MZVs, sometimes at the expense of an increase of depth by an even integer. This talk concerns the conjecture that the enumeration of MZVs that are not reducible to MZVs of lesser depth, yet are reducible to alternating sums of lesser depth, is generated by an enumeration of modular forms.

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