Zeta-like multiple zeta values in positive characteristic

Huy Hung Le (1) , Tuan Ngo Dac (2, 1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 CNRS - Centre National de la Recherche Scientifique

We study multiple zeta values (MZV's) over the rational function field over Fq which were introduced by Thakur as analogues of classical multiple zeta values of Euler. In this paper we affirmatively solve a conjecture of Lara Rodriguez and Thakur which gives a full list of zeta-like MZV's of weight at most q^2 and depth 2. Further, we completely determine all zeta-like MZV's of weight at most q^2 and arbitrary depth. Our method is based on a criterion which is derived from the Anderson-Thakur motivic interpretation of MZV's and the Anderson-Brownawell-Papanikolas criterion for linear independence in positive characteristic.

Mots clés: Function field arithmetic; Drinfeld and Anderson modules; t-motives; multiple zeta values

Domaines: Théorie des nombres [math.NT]

Huy Hung Le, Tuan Ngo Dac. Zeta-like multiple zeta values in positive characteristic. Mathematische Zeitschrift, 2022, 301, pp.2037-2057. ⟨10.1007/s00209-022-02970-4⟩. ⟨hal-03093398v2⟩