Wednesday, May 9 2018
16:45 - 17:45

#### One of the famous unsolved problems in number theory is Dedekind's conjecture, which says that $\zeta_K(S)/\zeta_F(s)$ is entire, where $\zeta_K(s)$ and $\zeta_F(s)$ denotes Dedekind zeta functions of K and F respectively. This motivates us to study quotients of $L$-functions. In this talk we shall discuss the holomorphy of quotients of Artin $L$-functions, using tools from representation theory of finite groups, notably Heilbronn characters which are certain virtual characters.

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