Tasaka’s conjecture on Z(3)
Let denote the finite multiple-zeta value corresponding to under the Kaneko–Zagier correspondence, defined from Bernoulli numbers, and let denote the quotient of the two solutions of the recurrence specified in Tasaka's conjecture. The conjecture asserts the identity . The supplied source does not state the recurrence, the initial conditions, or the precise meaning of the quotient in sufficient detail to expand this formulation further.
References
Primary source
Additional references
- A q-recurrence for a finite Apéry limit — arXiv — Henrik Bachmann
Progress summary
A September 2026 preprint claims to settle a specific case of the finite and symmetric multiple-zeta correspondence, but the claim has not been independently verified.
Tasaka’s conjecture concerns the relation between and solutions of a recurrence, as a concrete case of the finite/symmetric multiple-zeta correspondence predicted by the Kaneko–Zagier framework. The latest report says this relation is proved and yields further limits at roots of unity.
September 2026 claimed proof
Henrik Bachmann’s preprint A q-recurrence for a finite Apéry limit is reported to prove the conjectured relation, then derive algebraic and analytic limits at roots of unity. This is a claimed resolution of the tracked case, but no independent verification, error report, or withdrawal was found.
Current status (as of September 2026): the case is claimed solved but remains unverified; the full Kaneko–Zagier conjecture remains open.
Solutions 0
No solutions have been posted yet.