Abstract: The theory of L-functions lies at the heart of the Langlands program and in this talk we will focus on their building blocks, the local L-factors.
To be more precise, we will recall in the first part of the talk the Godement-Jacquet L-factors over complex numbers and their generalization to fields of more arbitrary characteristics.
In the second part we will explicitly compute these L-factors of irreducible representations of the general linear group over a local, non-archimedean field in terms of their C-parameters, a modular version of the Langlands parameters.
We approach the problem by extending the theory of Minguez and Jantzen of square-irreducible cuspidal representations and their derivatives to modular representations.