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Analytic Number Theory (AnNum)
Provider: Faculty of Science

Activity no.: 5588-20-07-31 
Enrollment deadline: 16/11/2020
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time16.11.2020, at: 08:00 - 29.01.2021, at: 16:00
Regular seats50
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserMorten S. Risager    E-mail address: risager@math.ku.dk
Written languageEnglish
Teaching languageEnglish
Semester/BlockBlock 2
Scheme groupA (Tues 8-12 + Thurs 8-17)
Exam formOral examination
Exam formOral examination
Exam detailsOral examination, 20 minutes with 20 minutes preparation time. All aids allowed.
Course workload
Course workload categoryHours
Lectures28.00
Exercises14.00
Exam50.00
Preparation114.00
Sum206.00
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
- 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

Literature
See Absalon

Target group

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

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