Funções aritméticas e teoremas elementares na distribuição dos números primos.

Abstract

This work aims at the study of arithmetic functions and the study of elementary theorems about the distribution of numbers. primes in which, first, the arithmetic functions and the Dirichlet product, the Euler function, Möbius function and its inverse, relations between functions, among others. Soon they will be studied the averages of arithmetic functions, passing through the Euler sum formula, asymptotic formulas and the average order of some functions. Finally, some elementary theorems about the distribution of prime numbers, Chebysshev functions and equivalent forms of the prime number theorem, Shapiro’s Tauberian theorem and applications and partial sums of the Möbius function will be discussed.