Modular forms, elliptic curves, p-Adic numbers and an almost integer number

• Grant number: 16/23059-9
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: January 01, 2017
• End date: December 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Herivelto Martins Borges Filho
• Grantee: Eduardo Rocha Walchek
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

In this project, we propose to study topics of the modular forms theory, elliptic curves (in particular, complex multiplication) and p-adic numbers (including the Tate curve) and, as an application, to justify the almost integrality of the number exp(pi sqrt(163)) in two different ways. (AU)