# Algebra/Number Theory Seminar

## On linear independence among special values of Thakur hypergeometric functions

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.