We introduce an
-adic
analogue of Gauss’s hypergeometric function arising from the Galois action on the
fundamental torsor of the projective line minus three points. Its definition is
motivated by a relation between the KZ equation and the hypergeometric differential
equation in the complex case. We show two basic properties, analogues of
Gauss’s hypergeometric theorem and of Euler’s transformation formula for our
-adic
function. We prove them by detecting a connection of a certain two-by-two matrix
specialization of even unitary associators with the associated gamma function, which
extends the result of Ohno and Zagier.
