11:50 am - 1:05 pm, Seminar Hall
MSc RESEARCH SEMINAR TALK
Heilbronn characters and their applications to the zeros of Artin L-function
Chennai Mathematical Institute.
We shall first introduce Artin L-functions, which are L-functions associated to representations of finite Galois groups. We then consider thes "Artin's holomorphy conjecture", which says that such L-functions associated to irreducible representations extend to entire functions. We shall discuss how to get meromorphic continuation and as a consequence, establish a conjecture of Dedekind on zeta functions. Motivated by the innovative work of Heilbronn, we shall introduce Heilbronn characters and use it to show a special case of Dedekind's conjecture, studying order of zeros of Artin L-functions.