structural:expansion, information:classification
L-functions

The Dirichlet L-series for a character χ {\displaystyle \chi } is

This series only converges for R s > 1 {\displaystyle {\mathfrak {R}}s>1}; it can be analytically continued to a meromorphic function

Dirichlet introduced the L {\displaystyle L} -function along with the characters in his 1837 paper.