NMAK14006U Analytic number theory (AnTal)
MSc Programme in Statistics
MSc Programme in Mathematics-Economics
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.
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
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.
- Category
- Hours
- Exam
- 50
- Exercises
- 14
- Lectures
- 28
- Preparation
- 114
- Total
- 206
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- Credit
- 7,5 ECTS
- Type of assessment
- Oral examination, 20 minutesOral 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.
Course information
- Language
- English
- Course code
- NMAK14006U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 2
- Schedule
- C (Mon 13-17 + Wednes 8-17)
- Course capacity
- No limit
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Course responsibles
- Morten S. Risager (7-746b7563696774426f63766a306d7730666d)
Phone: +45 3532 0756