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Probabilidades y distribución de los números primos

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Autor: Valladares Herrera, Francisco José
Director: Arias de Reyna Martínez, Juan
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2017-06
Tipo de documento: Trabajo Fin de Grado
Titulación: Universidad de Sevilla. Grado en Matemáticas
Resumen: In this project, we will try to study the prime factors of a number taken at random. The main objective will be to introduce the probabilistic theory of numbers and, at the same time, several central themes of probability theory in general: expected value, variance and the central limit. The story of probabilistic number theory begins with Hardy and Ramanujan, who were the ones who pushed the study of the central theme of this project: the distribution of ω(n), the number of prime divisors of a natural number n. Later generations, the area continued to develop remarkably with Erdös and Kac’s theorem (which is the main theme we will try to demonstrate and understand) until this day, thanks to both number theory specialists and probability experts. We will not assume any knowledge of complex analysis or measure theory. We only need to consider finite spaces of probability, so that we will start by studying expected value by treating ω as a random variable, using Chebyshev’s inequality...
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Cita: Valladares Herrera, F.J. (2017). Probabilidades y distribución de los números primos. (Trabajo Fin de Grado Inédito). Universidad de Sevilla, Sevilla.
Tamaño: 1.005Mb
Formato: PDF

URI: http://hdl.handle.net/11441/63199

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