ON THE ALGEBRAIC INDEPENDENCE OF LOGARITHMS OF ANDERSON t-MODULES

In the present paper, we determine the algebraic relations among the tractable coordinates of logarithms of Anderson t-modules constructed by taking the tensor product of Drinfeld modules of rank r defined over the algebraic closure of the rational function field and their (r -1)th exterior powers with the Carlitz tensor powers.Our results, in the case of the tensor powers of the Carlitz module, generalize the work of Chang and Yu Adv.Math.216(1) (2007), 321-345 on the algebraic independence of polylogarithms.Later, Anderson And86 extended the notion of Drinfeld modules to higher-dimensional objects, called t-modules (over L) of dimension s, which are tuples G = ( s a/L , ) of the s-copies of the additive group scheme a/L over L and an q -algebra homomorphism ∶ A → Mat s (L) given by