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Honorary MZVs and modular forms

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If you have a question about this talk, please contact Mustapha Amrani.

Grothendieck-Teichmller Groups, Deformation and Operads

$ um_{a>b>c>d>e>0}(-1)/(a3b6c3d6e3)$ 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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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