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.

Education

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

Learning outcome


Knowledge:
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.


Skills: 
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. 


Competences: 
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

Academic qualifications equivalent to a BSc degree is recommended.

Written
Oral
Individual
ECTS
7,5 ECTS
Type of assessment
Oral examination, 20 minutes
Type of assessment details
Oral examination with 20 minutes preparation time
Aid
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
  • Preparation
  • 114
  • Exercises
  • 14
  • Exam
  • 50
  • English
  • 206

Kursusinformation

Language
English
Course number
NMAK16001U
ECTS
7,5 ECTS
Programme level
Full Degree Master
Duration

1 block

Placement
Block 2
Schedulegroup
A
Capacity
No limit.
The number of seats may be reduced in the late registration period
Studyboard
Study Board of Mathematics and Computer Science
Contracting department
  • Department of Mathematical Sciences
Contracting faculty
  • Faculty of Science
Course Coordinator
  • Morten S. Risager   (7-79707a686e6c794774687b6f35727c356b72)
Saved on the 28-02-2022

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