NMAK23000U Advanced Number Theory

Volume 2023/2024

MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject


The goal of this course is to discuss some contemporary topics in number theory, such as automorphic forms and representations and their L-functions which constitute a very active area of research in modern number theory. Their theory generalizes and provides a common framework for classical number theoretic objects such as holomorphic and analytic modular forms, Dirichlet characters and their L-functions. Some connections to arithmetic geometry, spectral theory, or ergodic theory might also be discussed. A good background in analytic or algebraic number theory is recommended.

Learning Outcome

Knowledge: To display knowledge of the course topics and content, at the level of a beginning researcher.

Skills: To be able to use the acquired knowledge to obtain proofs.

Competences: To be able to produce independent proofs in extension of the acquired knowledge.


See Absalon for a list of course literature.

At least one of the courses Analytic Number Theory or Algebraic Number Theory.
Academic qualifications equivalent to a BSc degree are recommended.
4 hours of lectures and 2 hours of exercises per week.
  • Category
  • Hours
  • Lectures
  • 32
  • Preparation
  • 157
  • Theory exercises
  • 16
  • Exam
  • 1
  • Total
  • 206
Continuous feedback during the course of the semester
7,5 ECTS
Type of assessment
Oral examination, 30 min
Type of assessment details
30 minutes oral exam without preparation.
Exam registration requirements

To be able to attend the exam, the student must prepare and give at least one  30min talk during the course. The subject of the talk will be determined by the course responsible(s).

Without aids
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner

30 minutes oral exam without preparation. If no 30 min talk during the course was given, such a talk needs to be prepared and given no later than a week before the re-exam.

Criteria for exam assesment

The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.