We establish the existence of congruences between a fixed endoscopic, globally generic, cuspidal automorphic representation Π GSp(4) square-free conductor and stable representations same weight modulo certain prime factors value at 1 adjoint L-function Π, normalized by suitable period.

Irreducible representations are the building blocks of general, semisimple Galois representations ρ, and cuspidal representations are the building blocks of automorphic forms π of the general linear group. It is expected that when an object of the former type is associated to one of the latter type, usually in terms of an identity of L-functions, the irreducibility of the former should imply th...

We describe a new method to estimate the trilinear period on automorphic representations of PGL2(R). Such a period gives rise to a special value of the triple L-function. We prove a bound for the triple period which amounts to a subconvexity bound for the corresponding special value of the triple L-function. Our method is based on the study of the analytic structure of the corresponding unique ...

This essay contains somewhat dry material most useful in motivating eventually a certain crucial but at first sight somewhat technical transition from representations of groups to representations of Lie algebras. Parts of it will also be used in the theory of automorphic forms. I have made some effort to reduce everything to well known facts inmeasure theory and topology. The standard reference...

This essay contains somewhat dry material most useful in motivating eventually a certain crucial but at first sight somewhat technical transition from representations of groups to representations of Lie algebras. Parts of it will also be used in the theory of automorphic forms. I have made some effort to reduce everything to well known facts inmeasure theory and topology. The standard reference...

We prove an automorphic analogue of Deligne's conjecture for symmetric fourth L-functions Hilbert modular forms. extend the result Morimoto [41] based on generalization and refinement results Grobner Lin [18] to cohomological irreducible essentially conjugate self-dual cuspidal representations GL2 GL3 over CM-fields.

Let ∧ : GLn(C) −→ GLN (C), where N = n(n−1) 2 , be the map given by the exterior square. Then Langlands’ functoriality predicts that there is a map from cuspidal representations of GLn to automorphic representations of GLN , which satisfies certain canonical properties. To explain, let F be a number field, and let A be its ring of adeles. Let π = ⊗ v πv be a cuspidal (automorphic) representatio...

We consider the Fourier expansions of automorphic forms on general Lie groups, with a particular emphasis on exceptional groups. After describing some principles underlying known results on GL(n), Sp(4), and G2, we perform an analysis of the expansions on split real forms of E6 and E7 where simplifications take place for automorphic realizations of real representations which have small Gelfand-...