Analytic Langlands correspondence for $$PGL_2$$ on $${\mathbb {P}}^1$$ with parabolic structures over local fields

Abstract

AbstractWe continue to develop the analytic Langlands program for curves over local fields initiated in our earlier papers, following a suggestion of Langlands and a work of Teschner. Namely, we study the Hecke operators which we introduced in those papers in the case of a projective line with parabolic structures at finitely many points for the group $$PGL_2$$ P G L 2 . We establish most of our conjectures in this case.