The multiple zeta value data mine
The authors provide a data mine of proven results for Multiple Zeta Values (MZVs) and Euler sums. They investigate the Euler sums to weight \(w=12\) completely, deriving basis-representations for all individual values in an explicit analytic calculation. For the MZVs the same analysis is being performed up to \(w=22\). To \(w=24\) they checked the conjectured size of the basis using modular arithmetic. Under the further conjecture that the basis elements can be chosen out of MZVs of depth \(d\leq \frac{w}{3}\) they confirm the conjecture up to \(w=26\). The following runs at limited depth, using modular arithmetic keeping the highest weight terms only, were performed: \(d=7, w=27;d=6,w=28;d=7,w=29;d=6,w=30\). For the Euler sums complete results were obtained for \(d\leq 3,w=29;d\leq 4,w=22;d\leq 5,w=17\) and for \(d\leq 3,w=51;d\leq 4,w=30;d\leq 5,w=21;d\leq 6,w=17\) using modular arithmetic neglecting products of lower weight.
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