ALGEBRAIC INDEPENENCE OF CERTAIN FORMAL POWER SERIES (II)

Abstract

We shall extend the results of [5] and prove that if f = Z o a x ? Z [[X]] is
algebraic over Q (x), where a = 1, ƒ 1 and if ? , ? ,..., ? are p-adic integers, then 1 ? , ? ,..., ? are linkarly independent over Q if and only if (1+x) ,(1+x) ,…,(1+x) are algebraically independent over Q (x) if and only if f , f ,.., f are algebraically independent over Q (x)