We present a regularization procedure of period integrals automorphic forms on group $G$ over an arbitrary reductive subgroup $G' \subset G$. As consequence we obtain explicit $G'(\mathbb{A})$-invariant functional the space whose exponents avoid certain prescribed hyperplanes. also provide necessary and sufficient condition for convergence in terms their exponents.

We look at genera of even unimodular lattices rank 12 over the ring integers $${{\mathbb {Q}}}(\sqrt{5})$$ and 8 {Q}}}(\sqrt{3})$$ , using Kneser neighbours to diagonalise spaces scalar-valued algebraic modular forms. conjecture most global Arthur parameters, prove several them theta series, in manner Ikeda Yamana. find instances congruences for non-parallel weight Hilbert Turning genus Hermiti...

Let ζ5 be a primitive fifth root of unity, and let F = Q(ζ5). In this talk we describe recent computational work that investigates the modularity of elliptic curves over F . Here by modularity we mean that for a given elliptic curve E over F with conductor N there should exist an automorphic form f on GL2, also of conductor N , such that we have the equality of partial L-functions LS(s, f) = LS...

We prove new modularity lifting theorems for p-adic Galois representations in situations where the methods of Wiles and Taylor–Wiles do not apply. Previous generalizations of these methods have been restricted to situations where the automorphic forms in question contribute to a single degree of cohomology. In practice, this imposes several restrictions – one must be in a Shimura variety settin...

This paper describes the lifting of automorphic characters of O(3)(A) to S̃L2(A). It does so by matching the image of this lift with the lift of automorphic characters from O(1)(A) to S̃L2(A). Our matching actually gives a matching of individual automorphic forms, and not just of representation spaces. Let V be a 3− dimensional quadratic vector space and U a certain 1− dimensional quadratic space...

The homotopy type and homotopy groups of some spectra TAFGU of topological automorphic forms associated to a unitary similitude group GU of type (1, 1) are explicitly described in quasi-split cases. The spectrum TAFGU is shown to be closely related to the spectrum TMF in these cases, and homotopy groups of some of these spectra are explicitly computed.

A lifting map from cuspidal automorphic representations of the Jacobi group G J to cuspidal auto-morphic representations of the group PGL(2) is constructed. The lifting also has a local deenition, and the local and global versions are compatible. The local lifts can be described in terms of equivalence classes of local representations. The main idea in the construction is to exploit the close r...