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Title: La corba de Szegő
Author: Dalmau Ribas, Emma
Director/Tutor: Massaneda Clares, Francesc Xavier
Keywords: Teoria geomètrica de funcions
Treballs de fi de grau
Funcions enteres
Geometric function theory
Bachelor's theses
Entire functions
Issue Date: 21-Jan-2023
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 $S$.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Francesc Xavier Massaneda Clares
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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