Speaker: Mark Watkins Title: Dirichlet and Hecke characters and L-functions therein Time & Place: 4-5pm, Thursday 27 August, Carslaw 535 Abstract: Dirichlet originally used Dirichlet characters to show that every admissible arithmetic progression in the integers has infinitely many primes. These were then generalised by Hecke to number fields, where an analogous result is the Chebatorev density theorem concerning splitting behaviour of ideals. With regard to class field theory, one can additionally put prescribe a norm-component, which leads to the so-called Hecke Grossencharacters, which are still multiplicative, though no longer of finite order. These turn out to be related to arithmetic (particularly complex multiplication) in various guises. We give a leisurely introduction to this theory, explaining what is now implemented in Magma.