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arXiv · 2205.07165

Zagier-Hoffman's conjectures in positive characteristic

Bo-Hae Im·Hojin Kim·Khac Nhuan Le·Tuan Ngo Dac·Lan Huong Pham
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Abstract

Multiples zeta values and alternating multiple zeta values in positive characteristic were introduced by Thakur and Harada as analogues of classical multiple zeta values of Euler and Euler sums. In this paper we determine all linear relations among alternating multiple zeta values and settle the main goals of these theories. As a consequence we completely establish Zagier-Hoffman's conjectures in positive characteristic formulated by Todd and Thakur which predict the dimension and an explicit basis of the span of multiple zeta values of Thakur of fixed weight.

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Bo-Hae Im, Hojin Kim, Khac Nhuan Le, Tuan Ngo Dac, Lan Huong Pham. 2022-05-15. Zagier-Hoffman's conjectures in positive characteristic. https://arxiv.org/abs/2205.07165

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