Symmetric power functoriality for holomorphic modular forms

Abstract: Langlands’s functoriality conjectures predict the existence of "liftings" of automorphic representations along morphisms of L-groups. A basic case of interest comes from the irreducible algebraic representations of GL(2), thought of as the L-group of the reductive group GL(2) over Q. I will discuss the proof, joint with James Newton, of the existence of the corresponding functorial liftings for a broad class of holomorphic modular forms, including Ramanujan’s Delta function.

number theory

Audience: researchers in the topic

UCLA Number Theory Seminar