Alternating double-zeta reduction conjecture

About 9 years old · traced to

Let mm be a positive integer, and let ζ(r‾,s)\zeta(\overline{r},s) denote an alternating double zeta value, while a non-alternating double zeta value has no barred index. Alternating double-zeta reduction conjecture. The combined sum

ζ(2m‾,2)+2mζ(2m+1‾,1)\zeta(\overline{2m},2)+2m\zeta(\overline{2m+1},1)

can be expressed in terms of non-alternating double zeta values.

This conjecture predicts that a particular family of alternating double-zeta combinations reduces to non-alternating values. No proof or resolution is supplied in the excerpt.

References

Primary source

Ce Xu, “Evaluations of nonlinear Euler sums of weight ten”, arXiv:1703.00254 (2017).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.