ON THE ALGEBRAIC INDEPENDENCE OF LOGARITHMS OF ANDERSON t-MODULES

抄録

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 ten- sor 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.