NMAK14006U Analytic number theory (AnTal)

Volume 2014/2015
Education
MSc Programme in Mathematics
MSc Programme in Statistics
MSc Programme in Mathematics-Economics
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.

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 

 

  1. Analyze and prove results presented in analytic number theory
  2. Prove results similar to the ones presented in the course
  3. 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

 

 

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

 

H.L. Montgomery and R.C. Vaughan. Multiplicative number theory. I. Classical theory, volume 97 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 2007. 

Supplementary notes might also be used.

Complex Analysis (KomAn) or equivalent
Weekly: 4 hours of lectures and 2 hours of exercises for 7 weeks.
  • Category
  • Hours
  • Exam
  • 50
  • Exercises
  • 14
  • Lectures
  • 28
  • Preparation
  • 114
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Oral examination, 20 minutes
Oral examination with 20 minutes preparation time
Exam registration requirements
To be allowed to take the oral exam the student should have at least 3 out of 4 hand-in exercises approved.
Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners
Criteria for exam assesment

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