In 1995, Thakur defined and studied positive characteristic analogues of hypergeometric functions. He found their properties, such as specializations to Carlitz exponential functions, Bessel-Carlitz functions, the existence of contiguous, summation formulae and so on. But it was not known whether they are related with periods or not unlike the characteristic 0 case. In this talk, we give period interpretation for special values of Thakur’s hypergeometric functions via pre-$t$-motives. As applications of this interpretation and Chang’s refined Anderson-Brownawell-Papanikolas criterion, we illustrate linear independence results among these special values with some distinct parameters and algebraic points.

If time permits, we briefly introduce by-products, linear/algebraic independence results among Kochubei polylogarithms and their generalizations at algebraic points.