Correction to "Computational Complexity of Algebraic Functions"

In the author’s paper [ 11, the proof of Proposition 5.2 is erroneous. Specifically, the assertion immediately preceding the proposition is false, and the proof of the proposition given in [ 1 ] relies on this assertion. The object of this note is to give a correct proof of Proposition, 5.2 of [ 11. Essentially the same error is made in the subsequent paper [2] of Ja’ Ja’, in the proof of Lemma 3.2. We shall also give a correct proof of Lemma 3.2 of [2]. Let C be a function that assigns to every positive integer d a non-negative real number C(d) and satisfies the following three axioms.