Algebraic independence on T-modules

We study the transcendence degree (of the values at algebraic points) of th e coordinate functions of a given one parameter subgroup on a simple g dime nsional T-module. In such a situation, we obtain a lower bound for this tra nscendence degree depending on g and on the growth order of the parameter s ubgroup. As a particular case, one gets the finite characteristic analogue of a result of Siegel on the algebraic independence for the values of the c lassical Bessel function.