Abstract

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