Hecke characters are analogues of Dirichlet characters for number fields. Letting the field K and the character \(\chi \) vary gives a family of L-functions \(L(s,\chi )\) subsuming both Dirichlet L-functions ( \(K=\mathbb {Q}\) ) and Dedekind zeta functions ( \(\chi =1\) ). In his 1950 Princeton PhD thesis [Tat50], completed under Emil Artin, John Tate found an extremely elegant way of deriving the analytic properties of all the \(L(s,\chi )\) collectively.