Hopf algebras and multiple zeta values in positive characteristic

Abstract

Multiples zeta values (MZV's for short) in positive characteristic were introduced by Thakur as analogues of classical multiple zeta values of Euler. In this paper we give a systematic study of algebraic structures of MZV's in positive characteristic. We construct both the stuffle algebra and the shuffle algebra of these MZV's and equip them with algebra and Hopf algebra structures. In particular, we completely solve a problem suggested by Deligne and Thakur \cite{Del17} in 2017 and establish Shi's conjectures \cite{Shi18}. The construction of the stuffle algebra is based on our recent work \cite{IKLNDP22}.

arXiv comment116 pages

References in corpus (7)

• Mixed Tate Motives and Multiple Zeta Values
• Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms
• Quasi-shuffle products revisited
• Quasi-shuffle products
• Linear independence of monomials of multizeta values in positive characteristic
• Multizeta values for F_q[t], their period interpretation and relations between them
• On motivic multiple $t$ values, Saha's basis conjecture, and generators of alternating MZV's

Cited by in corpus (1)

• Hopf algebras and alternating multiple zeta values in positive characteristic