$t$-motivic interpretations for special values of Thakur hypergeometric functions and Kochubei multiple polylogarithms

Abstract

In 1995, Thakur invented and studied positive characteristic analogues of hypergeometric functions. In this paper, we interpret the special values of those functions by rigid analytic trivializations for some pre-$t$-motives. As a consequence, we show their transcendence and linear independence results by using Chang’s refined version of the Anderson–Brownawell–Papanikolas criterion. Furthermore, we show some linear independence results among the special values of Kochubei multiple polylogarithms according to our $t$-motivic interpretation and the corresponding refined criterion.