Normality of product expansions of power series over finite fields (Q1184896)

Given an infinite power series \(y=1+\sum c_ r x^ r\) (\(r\geq 1\)), a product representation \(y=\prod_{n=1}^{+\infty}(1+a_ n x^ n)\) is studied, where \(a_ n\) and \(c_ r\) belong to some finite field. It is shown that the coefficients \(a_ n=a_ n(y)\) form a normal sequence for almost all power series with respect to Haar measure. In the limit theorems behind this statement, error terms are estimated, and some asymptotic distributional results are established.