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Results tagged with automorphic-forms
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An automorphic form is a well-behaved function from a topological group $G$ to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup $\Gamma \subset G$ of the topological group. Automorphic forms are a generalization of the idea of periodic functions in Euclidean space to general topological groups.
12
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Accepted
Sato-Tate measure for GL(3) Automorphic forms
(2017-11-26 edit by j.c.: earlier versions of this answer consisted of David Hansen's screenshot of the following, with the text "Here is a screenshot of a semi-answer which froze my computer when I h …
- 13.6k
8
votes
Langlands in dimension 2: the Yoshida conjecture
There's no need to require irreducibility. If $A=E_1 \times E_2$ is a product of elliptic curves the conjecture is true, by modularity of elliptic curves combined with Yoshida's lifting from pairs of …
- 13.1k
2
votes
Terminology occuring in automorphic representation and relationship between them
For global automorphic representations, square-integrable is weaker than cuspidal. According to Moeglin-Waldspurger, the square-integrable automorphic representations of $GL_n(\mathbb{A})$ are genera …
- 13.1k
5
votes
Overview of automorphic representations for $SL(2)/{\mathbf{Q}}$?
The multiplicity of any cusp form in the spectrum is one; this follows from the analysis in LL and the results proven in Ramakrishnan's paper "Modularity of the Rankin-Selberg L-series and multiplici …
- 13.1k
15
votes
Where stands functoriality in 2009?
The work of Ngo should allow for the treatment of all endoscopic cases of functoriality; this is a kind of technical condition, but includes transfer from classical groups to GL(n) and base change for …
- 13.1k