Year: 2026
Type: preprint
Abstract: The Kaneko-Zagier conjecture predicts a correspondence between finite and symmetric multiple zeta values. Under this correspondence, $ζ(3)$ corresponds to an element $Z(3)$ defined by Bernoulli numbers. We prove a conjecture of Tasaka relating $Z(3)$ to the quotient of two solutions of a recurrence. A two-index $q$-recurrence connects this quotient to a finite harmonic $q$-series. Using a method of the author, Takeyama, and Tasaka, we obtain the algebraic and analytic limits $3Z(3)/4$ and $3ζ(3)/4$ at roots of unity.
Source: arXiv (Cornell University)
Author: Bachmann, Henrik
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213506712