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.

We derive a precise relation of poles Eisenstein series associated to the cuspidal datum $\chi\otimes\sigma$ and lowest occurrence theta lifts automorphic representation $\sigma$ unitary group, where $\chi$ is conjugate self-dual character. A key ingredient proof computation period integrals truncated series.

‎In the spirit of the Langlands proposal on  Beyond Endoscopy ‎we discuss the explicit relation between the Langlands functorial transfers and automorphic $L$-functions‎. ‎It is well-known that the poles of the $L$-functions have deep impact to the Langlands functoriality‎. ‎Our discussion also‎ ‎includes the meaning of the central value of the tensor product $L$-functions in terms of the Langl...

Let $$\pi $$ be a non-self-dual unitary cuspidal automorphic representation not of solvable polyhedral type for $$\mathrm{GL}(2)$$ over number field. We show that has positive upper Dirichlet density Hecke eigenvalues in any sector whose angle is at least 2.63 radians.

‎We first give bounds for domains where the unitarizabile subquotients can show up in the parabolically induced representations of classical $p$-adic groups‎. ‎Roughly‎, ‎they can show up only if the‎ ‎central character of the inducing irreducible cuspidal representation is dominated by the‎ ‎square root of the modular character of the minimal parabolic subgroup‎. ‎For unitarizable subquotients...

Recently, a new approach to functoriality of automorphic representations [L1] has been proposed in [FLN] following earlier work [L2, L3, L4] by Robert Langlands. The idea may be roughly summarized as follows. Let G and H be two reductive algebraic groups over a global field F (which is either a number field or a function field; that is, the field of functions on a smooth projective curve X over...

This paper is concerned with a compatible family of 4-dimensional -adic representations ρ of GQ := Gal(Q/Q) attached to the space of weight-3 cuspforms S3(Γ) on a noncongruence subgroup Γ ⊂ SL2(Z). For this representation we prove that: 1. It is automorphic: the L-function L(s, ρ∨ ) agrees with the L-function for an automorphic form for GL4(AQ), where ρ ∨ is the dual of ρ . 2. For each prime p ...

Let X be an even dimensional symmetric bilinear space defined over a totally real number field F with adeles A, and let σ = ⊗vσv be an irreducible tempered cuspidal automorphic representation of O(X,A). We give a sufficient condition for the nonvanishing of the theta lift Θn(σ) of σ to the symplectic group Sp(n,A) (2n by 2n matrices) for 2n ≥ dimX for a large class of X. As a corollary, we show...

We consider d=4, N = 2 compactifications of heterotic strings with an arbitrary number of Wilson lines. In particular, we focus on known chains of candidate heterotic/type II duals. We give closed expressions for the topological amplitudes F (g) in terms of automorphic forms of SO(2 + k, 2,Z), and find agreement with the geometric data of the dual K3 fibrations wherever those are known. a marle...

Let X be a smooth projective connected curve over an algebraically closed field k of positive characteristic. Let G be a reductive group over k, γ be a dominant coweight for G, and E be an l-adic Ǧ-local system on X , where Ǧ denotes the Langlands dual group (over Q̄l). Let BunG be the moduli stack of G-bundles on X . Under some conditions on the triple (G, γ,E) we propose a conjectural construc...