In this paper, we study the linear independence of special values, including the positive characteristic analogue of multizeta values, alternating multizeta values and multiple polylogarithms, at algebraic points. Consequently, we establish linearly independent sets of these values with the same weight indices and a lower bound on the dimension of the space generated by depth r > 2 multizeta values of the same weight in positive characteristic.

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In this article, we prove the integrality of v-adic multiple zeta values (MZVs). For any index s ∈ N r and finite place v ∈ A := Fq[θ], Chang and Mishiba introduced the notion of the v-adic MZVs ζA(s)v, which is a function field analogue of Furusho's p-adic MZVs. By estimating the v-adic valuation of ζA(s)v, we show that ζA(s)v is a v-adic integer for almost all v. This result can be viewed as a function field analogue of the integrality of p-adic MZVs, which was proved by Akagi-Hirose-Yasuda and Chatzistamatiou.