The odd-characteristic spanning conjecture for v-adic multiple zeta relations

Let K=Fq(t)K=\mathbb{F}_q(t) be a rational function field and let vv be a finite monic prime. Write Wv(K)W_v(K) for the vector space of vv-adic multiple zeta values at integer tuples. Odd-characteristic spanning conjecture. If char(Fq)2\operatorname{char}(\mathbb{F}_q)\neq 2, the linear relations over Fq\mathbb{F}_q in Wv(K)W_v(K) are spanned by the relations in Theorem 3 and by trivial zeros. This is the proposed complete description of the relations at a fixed prime in characteristics other than two; the supplied text gives no proof or resolution.

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Primary source

Qibin Shen, “Universal F_q-Family of v-adic Multiple Zeta Values over Function Fields”, arXiv:1912.10516 (2019).

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