La corba de Szegő

Abstract

[en] Around the year 1924, Hungarian mathematician Gábor Szegő found that the zeros of the $n$th partial sums of the exponential series, rescaled by $n$, accumulate on the curve $S=\left\{z \in \overline{\mathbb{D}}:\left|e^{1-z} z\right|=1\right\}$. Not only that, but he showed that this zeros are uniformly distributed around $S$ according to the variation of the argument of the entire function $h(z)=e^{1-z} z$. In this thesis we show these results and other later discoveries that specify the velocity of convergence and the distance from the zeros to $S$.