On the transcendence of special values of Goss L -functions attached to Drinfeld modules

Let [Formula: see text] be the finite field with [Formula: see text] elements and consider the rational function field [Formula: see text]. For a Drinfeld module [Formula: see text] defined over [Formula: see text], we study the transcendence of special values of the Goss [Formula: see text]-function attached to the abelian [Formula: see text]-motive [Formula: see text] of [Formula: see text]. Moreover, when [Formula: see text] is a Drinfeld module of rank [Formula: see text] defined over [Formula: see text] which has everywhere good reduction, we prove that the value of the Goss [Formula: see text]-function attached to the [Formula: see text]-st exterior power of [Formula: see text] at any positive integer is transcendental over [Formula: see text].