Víctor Hernández Barrios
Abstract
The aim of this thesis is to expose the basic theory of the Riemann zeta function and some of its classical applications in multiplicative number theory, like the prime number theorem and Dirichlet's theorem on arithmetic progressions. In the last chapter we prove Hardy's theorem, a result closely related with the Riemann hypothesis.
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The aim of this thesis is to expose the basic theory of the Riemann zeta function and some of its classical applications in multiplicative number theory, like the prime number theorem and Dirichlet's theorem on arithmetic progressions. In the last chapter we prove Hardy's theorem, a result closely related with the Riemann hypothesis.
Key concepts: Analytic number theory, Riemann zeta function, Prime number theorem, Mathematics, Riemann hypothesis, Multiplicative number theory, Multiplicative function, Riemann Xi function