Analytic Number Theory
Syllabus, Master's level, 1MA038
- Code
- 1MA038
- Education cycle
- Second cycle
- Main field(s) of study and in-depth level
- Mathematics A1N
- Grading system
- Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Finalised by
- The Faculty Board of Science and Technology, 15 March 2007
- Responsible department
- Department of Mathematics
Entry requirements
BSc with 90 credit points Mathematics including Complex Analysis
Learning outcomes
In order to pass the course (grade 3) the student should be able to
Higher grades, 4 or 5, require a higher level of proficiency. The student should be able to solve problems of greater complexity, i.e. problems requiring a combination of ideas and methods for their solution, and be able to give a more detailed account of the proofs of important theorems and by examples and counter-examples be able to motivate the scope of various results. Requirements concerning the student's ability to present mathematical arguments and reasoning are greater.
Content
Results concerning the distribution of primes obtained by elementary methods. Dirichlet characters. The zeta function and Dirichlet's L-function. A proof of the prime number theorem and the prime number theorem for arithmetic sequences. Explicit formulas for Chebychev's psi-function. Dirichlet's class number formula. Siegel's theorem. Bounds on sums of characters. Briefly about sieve methods and Bombieri's theorem.
Instruction
Lectures and problem solving sessions.
Assessment
Written and, possibly, oral examination at the end of the course. Moreover, compulsory assignments may be given during the course.
Reading list
- Reading list valid from Autumn 2022
- Reading list valid from Spring 2019
- Reading list valid from Spring 2014
- Reading list valid from Autumn 2013, version 2
- Reading list valid from Autumn 2013, version 1
- Reading list valid from Autumn 2010, version 2
- Reading list valid from Autumn 2010, version 1
- Reading list valid from Autumn 2008