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Level: MSci
Title: Dirichlet's theorem on arithmetic progressions
Supervisor:

Dr Ivan Tomasic
Research Area: Algebra
Description:

The theorem states that for two coprime integers a and b, the arithmetic sequence (a+nb:n\in N) contains infinitely many prime numbers, i.e., there are infinitely many primes congruent to a \mod b. The project would entail going through the second part of Serre's beautiful book 'A course in arithmetic' and studying the analytic methods of number theory used in the proof. An ambitious student might study further, in the direction of a more general theorem of Chebotarev.
Further Reading:

Literature suggestions will be supplied.
Key Modules:

To be confirmed with the supervisor.
Other Information:
Current Availability: Yes