Computational Algebra Seminar: Watkins -- Dirichlet and Hecke characters and L-functions therein

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.