Zagier-Hoffman's conjectures in positive characteristic

2022/05/15 by Im, Bo-Hae, Kim, Hojin, Le, Khac Nhuan +2
#11J93 #11M38 #11R58 #FOS: Mathematics #Number Theory (math.NT) #Primary 11M32 #Secondary 11G09

paper · doi:10.48550/arxiv.2205.07165

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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