Formas modulares e o problema dos números congruentes

• Ano de defesa: 2015
• Autor(a) principal: Reis, Alexandre Silva dos
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal do Espírito Santo; BR; Mestrado em Matemática; Centro de Ciências Exatas; UFES; Programa de Pós-Graduação em Matemática
• Palavras-chave em Português: Complex lattices; Elliptic curves; Modular forms; Congruent numbers; Números congruentes; Reticulados complexos; Formas modulares; Curvas elípticas; Teoria dos reticulados; Formas (Matemática); Matemática; 51
• Link de acesso: http://repositorio.ufes.br/handle/10/7509

Complex lattices, complex tori and elliptic curves are objects that although having different structures and nature, are equivalent. It is possible by means of a complex lattice to obtain a complex torus and hence, to obtain an elliptic curve; and that “path”’ can also be done in reverse. This connection will be the main object of study in this work, which will also address a careful manner some issues related to it, such as the special linear group, modular forms and modular curves. Finally, as an application of the concepts and tools studied, the congruent numbers problem is considered. This problem besides being closely related to elliptic curves, has a relationship with the famous Birch and Swinnerton-Dyer conjecture, one of the Millennium Problems.