On motivic multiple $t$ values, Saha's basis conjecture, and generators of alternating MZV's

Abstract

We give an evaluation for the stuffle-regularised $t^{\ast ,V}(\{2{\}}^a,1,\{2{\}}^b)$ as a polynomial in single-zeta values, $\log (2)$ and $V$. We then apply this to establish some linear independence results of certain sets of motivic multiple $t$ values. In particular, we prove the elements of Saha's conjectural basis are linearly independent, on the motivic level, and that the (suitably regularised) elements $t^{\mathfrak{m}}(\{1,2{\}}^{\times })$ form a basis for both the (extended) motivic MtV's and the alternating MZV's.

53 pages

Cited by in corpus (2)

• Hopf algebras and multiple zeta values in positive characteristic
• Hopf algebras and alternating multiple zeta values in positive characteristic