A Type Theorem for ∫z (t)/t dt and Applications to Entire Functions

Let P(z) = Σ a_kz^k be an entire series. Let M (r), n{r), v(r), and μ(r) stand, as usual [1] for the 'Maximum modulus' etc. of P and let I(r) be the 'logarithmic mean of P' viz. (l/2π) ∫ log|P(r e^tθ)| dθ.