LINDEMANN-WEIERSTRASS THEOREM FOR DRINFEL D MODULES

Let phi a F-q[T] Drinfeld module, with rank d > 0 and whose coefficien ts are algebraic over F-q(T). We denote Lambda and e(Lambda) the latti ce and the exponential function associated with phi, Omega the complex multiplication ring of Lambda, and d(1) = rank(Fq[T])Omega. Let alpha 1,...,alpha(n) epsilon F-q(T) linearly independent over Omega. We den ote t the transcendence degree over F-q(T) of the extension generated by e(Lambda) (alpha(1)),...,e(Lambda)(alpha(n)). Then the following in equality holds td greater than or equal to nd(1). This result is an an alogous for Drinfeld modules of the Lindemann-Weierstrass theorem.