Anderson–Thakur polynomials and multizeta values in positive characteristic

Multizeta values in positive characteristic were first introduced and studied by Thakur. He and Lara Rodríguez (“Zeta-like multizeta values for $\mathbb{F}_q [t]$”, Indian J. Pure Appl. Math., 45:5 (2014), pp. 785–798) discovered and conjectured certain zeta-like families. Kuan, Lin and Yu stated more conjectures about zeta-like multizeta values in “Criterion for deciding zeta-like multizeta values in positive characteristic” (to appear in Experimental Mathematica). In the present paper we study and give the transparent formula for certain Anderson–Thakur polynomials. This enables us to confirm the conjectured zeta-like families.

Keywords

multiple zeta values, zeta-like, Anderson-Thakur polynomials

2010 Mathematics Subject Classification

11J91, 11M32, 11M38

Full Text (PDF format)

Received 10 July 2015

Accepted 27 September 2016

Published 6 March 2018