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Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops
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abstract
It is found that the number, $M_n$, of irreducible multiple zeta values (MZVs) of weight $n$, is generated by $1-x^2-x^3=\prod_n (1-x^n)^{M_n}$. For $9\ge n\ge3$, $M_n$ enumerates positive knots with $n$ crossings. Positive knots to which field theory assigns knot-numbers that are not MZVs first appear at 10 crossings. We identify all the positive knots, up to 15 crossings, that are in correspondence with irreducible MZVs, by virtue of the connection between knots and numbers realized by Feynman diagrams with up to 9 loops.
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Cited by 1 Pith paper
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Higher-genus multiple zeta values
The paper defines higher-genus multiple zeta values, regularizes them via Schottky uniformization, and proves and conjectures new identities among them.
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