We construct an Euler system for Galois representations associated to cohomological cuspidal automorphic of $\operatorname{GSp}\_4$, using the pushforwards Eisenstein classes $\operatorname{GL}\_2 \times \operatorname{GL}\_2$.

Abstract We use the theta correspondence to study equivalence between Godement–Jacquet and Jacquet–Langlands L -functions for ${\mathrm {GL}}(2)$ . show that resulting comparison is in fact an expression of exotic symmetric monoidal structure on category -modules. Moreover, this enables us construct abelian abstractly automorphic representations, whose irreducible objects are usual representati...

Automorphic Lie Algebras are interesting because of their fundamental nature and their role in our understanding of symmetry. Particularly crucial is their description and classification as it allows us to understand and apply them in different contexts, from mathematics to physical sciences. While the problem of classification of Automorphic Lie Algebras with dihedral symmetry was already cons...

Abstract We find the number s k ⁢ ( p , Ω stretchy="false">) s_{k}(p,\Omega) of cuspidal automorphic representations GSp 4 mathvarian...

This paper is an expository account of our 1976 monograph [6] on Scattering theory for automorphic functions. Several improvements have been incorporated: a more direct proof of the meromorphic character of the Eisenstein series, an explicit formula for the translation representations and a simpler derivation of the spectral representations. Our hyperbolic approach to the Selberg trace formula ...

Automorphic forms play an important rôle in physics, especially in the realm of string and M-theory dualities. Notably, the hidden symmetries of 11-dimensional supergravity compactifications, discovered by Cremmer and Julia, motivate the study of automorphic forms for exceptional arithmetic groups En(Z) (including their n ≤ 5 classical A andD instances). These Notes are a pedestrian introductio...