Analytic Number Theory (AnNum)

Course content

The prime number theorem gives an estimate for the number of primes less than a given value x. This theorem - which we will prove - is intimately related to the location of the zeroes of the famous Riemann zeta function. We shall study the analytic properties of the Riemann zeta functions as well as more general L-function. We consider primes in arithmetic progressions, zero-free regions, the famous Riemann hypothesis, the Lindelöf hypothesis, and related topics.


MSc Programme in Mathematics

Learning outcome

At the end of the course students are expected to have a thourough knowledge about results and methods in analytic number theory as described under course content.

At the end of the course students are expected to be able to 

  • Analyze and prove results presented in analytic number theory
  • Prove results similar to the ones presented in the course
  • apply the basic techniques, results and concepts of the course to concrete examples and exercises. 

At the end of the course students are expected to be able to

  • Explain and reproduce abstract concepts and results in analytic number theory
  • Come up with proofs for result at the course level
  • discuss topics from analytic number theory


Weekly: 4 hours of lectures and 2 hours of exercises for 7 weeks.

Complex Analysis (KomAn) or equivalent

7,5 ECTS
Type of assessment
Oral examination, 20 minutes
Oral examination with 20 minutes preparation time
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners
Criteria for exam assessment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 28
  • Exercises
  • 14
  • Exam
  • 50
  • Preparation
  • 114
  • English
  • 206