#### Alladi Ramakrishnan Hall

#### Virtual Characters on the theory of Artin $L$-functions

#### Subham Bhakta

##### CMI Chennai

*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.*

Done