Marzo Sánchez, JordiArribas Viera, David2024-12-122024-12-122024-09-02https://hdl.handle.net/2445/217049Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2023-2024. Director: Jordi Marzo SánchezWe find minimizing configurations for most of the Riesz-$s$ energies on the unit circle $S^{1}$ . We also provide a complete asymptotic expansion of the Riesz-$s$ energy associated to $N$ equally spaced points on the $S^{1}$. Finally, we present Chui's conjecture, prove a partial result and show how it leads to an interesting consequence about function approximation in the Bergman space.50 p.application/pdfengcc by-nc-nd (c) David Arribas Viera, 2024http://creativecommons.org/licenses/by-nc-nd/3.0/es/Teoria del potencial (Matemàtica)Geometria convexaTreballs de fi de màsterFuncions de variables complexesPotential theory (Mathematics)Convex geometryMaster's thesisFunctions of complex variablesinfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccess