Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops

D. J. Broadhurst, D. Kreimer

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 $9\ge n\ge 3$, $M_n$ enumerates…