Sobre a distribuição dos Números Primos

Abstract

This work aims to study results about the distribution of prime numbers in which, initially, arithmetic functions, Dirichlet’s product, Mobius inversion formula, Euler’s sum formula, among others, will be defined. Then, the basic concepts necessary to prove the prime number theorem will be studied, such as the Riemann zeta function, the Chebyshev functions, Laplace transform, among others. Furthermore, Dirichlet’s theorem about primes in arithmetic progressions will be studied. Finally, basic concepts about sieve methods will be presented, such as the sieve of Eratosthenes and Legendre and the Rankin’s trick.