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Pré-Publication, Document De Travail Année : 2023

Hopf algebras and multiple zeta values in positive characteristic

Résumé

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 in 2017 and establish Shi's conjectures. The construction of the stuffle algebra is based on our recent work on Zagier-Hoffman's conjectures in positive charactertistic.
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Dates et versions

hal-03937702 , version 1 (13-01-2023)

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Bo-Hae Im, Hojin Kim, Khac Nhuan Le, Tuan Ngo Dac, Lan Huong Pham. Hopf algebras and multiple zeta values in positive characteristic. 2023. ⟨hal-03937702⟩
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