The focus of the course will be on prime number theory. We give a relatively simple proof of both the Prime Number Theorem and the Prime Number Theorem for arithmetic progressions, based on complex analysis. We discuss Dirichlet series, the Riemann zeta function, Dirichlet characters and L-functions, and other topics if time permits. More details are given on the home page of the course, see the link below.

**Hours/week**

2

**Examination**

4 graded homework assignments and oral exam. Both the average of the grades of the four assignments and the grade of the oral exam contribute for 50% to the final grade.

**Literature**

Lecture notes will be posted on the home page of the course.

**Prerequisites**

Abelian groups and maybe a little bit of ring theory (Algebra 1 and 2 in Leiden), convergence of series, uniform convergence and complex analysis

(Wiskundige structuren, Analyse 1,2,4 in Leiden). During the course we will recall the complex analysis that we need in our course and add a few topics that have not been treated in Analyse 4.

The prerequisites will be summarized in the lecture notes.

**Remark 1**

This course is suited for a master’s thesis project in number theory.

**Remark 2**

The course will not be given in 2015/16.

**Remark 3**

Information about the course is maintained on the Homepage Analytic Number Theory. We do not use the Blackboard-system.