MATM25 Specialised Course in Number Theory is an elective
course at advance level for a Master of Science degree in mathematics.
course gives an introduction to classical analytic number theory.
We introduce the Riemann zeta-function as well as more general
L-functions, and study their analytic
properties to reveal the distribution of primes, leading up to proofs
of the prime number theorem and Dirichlet's theorem on primes in
arithmetic progressions. If time permits, further topics in analytic number theory are covered, such as sieve theory.
The teaching consists mainly of lectures. Compulsory hand-in exercises may be given.
The module is assessed through written assignments and an oral examination.
There is no compulsory course literature, but if you
want some complement to the material presented in the lectures, here
are some suggestions:
- Harold Davenport: Multiplicative Number Theory. (Classic, but quite demanding)
- Tom M. Apostol: Introduction to Analytic Number Theory (Easier, aimed at undergraduates)
Lecture notes (freely available):
- Terry Tao's lecture notes (available on his blog). Here is a link to part 1.
- Andreas Strömbergsson's lecture notes based on Davenport's book. link
- Noam Elkies' lecture notes. link
The schedule is available in the TimeEdit schedule tool. For instructions on how to use TimeEdit click here.