Faculty of Science

Analytic Number Theory (AnNum)
Provider: Faculty of Science

Activity no.: 5588-20-07-31
	Enrollment deadline: 16/11/2020

Place

Department of Mathematical Sciences

Date and time

16.11.2020, at: 08:00 - 29.01.2021, at: 16:00

Regular seats

ECTS credits

7.50

Contact person

Nina Weisse E-mail address: weisse@math.ku.dk

Enrolment Handling/Course Organiser

Morten S. Risager E-mail address: risager@math.ku.dk

Written language

English

Teaching language

English

Semester/Block

Block 2

Scheme group

A (Tues 8-12 + Thurs 8-17)

Exam form

Oral examination

Exam form

Oral examination

Exam details

Oral examination, 20 minutes with 20 minutes preparation time. All aids allowed.

Course workload

Course workload category	Hours
Lectures	28.00
Exercises	14.00
Exam	50.00
Preparation	114.00

Sum	206.00

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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