Zeros of normalized sections of non convergent power series (Q2302309)

In this interesting article the author gives a necessary and sufficient condition so that the sequence of the normalized sections of a power series \(\displaystyle\sum_{n=0}^{+\infty}a_nz^n\), with zero radius of convergence, belongs to the Szegő class. Note that the sequence of the normalized sections of a power series \(\displaystyle\sum_{n=0}^{+\infty}a_nz^n\) with zero radius of convergence is the sequence of polynomials \(\displaystyle p_n(z)=\sum_{k=0}^{n}a_k A_n^{-k}z^k, \ n\in\mathbb{N}\), where \(\displaystyle A_n=\max_{1\leq k\leq n}|a_k|^{\frac{1}{k}}, \ n\in\mathbb{N}\). Note, in addidtion, that a sequence of polynomials \((p_n)_n\) belongs to the Szegő class, if and only if, a certain condition holds for a specific sequence of functions \((v_n)_n\), which count the zeros of \(p_n\).