Arithmetical functions, Euler products and the zeta function

Lecturer: Diego de la Fuente

Date: 10/09/2018

Time: 15:00

Place: Room 209 (2nd floor, Faculty of Mathematics UCM)

Abstract:

An arithmetical function maps values in N to values in C or R. First of all, we are going to expose some examples and properties of them. In spite of their simplicity, arithmetical functions are powerful, with them you can prove Dirichlet theorem for arithmetic progressions or the prime number theorem.

We will define Dirichlet convolutions, the inverse and derivative of this operation to operate over arithmetical functions and we will demonstrate the Euler product and a theorem about product of series Dirichlet to relate these functions with zeta function.

Bibliography

• Tom M. Apostol, Introduction to analytic number theory.

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