Skip to main content
Search type Search syntax
Tags [tag]
Exact "words here"
Author user:1234
user:me (yours)
Score score:3 (3+)
score:0 (none)
Answers answers:3 (3+)
answers:0 (none)
isaccepted:yes
hasaccepted:no
inquestion:1234
Views views:250
Code code:"if (foo != bar)"
Sections title:apples
body:"apples oranges"
URL url:"*.example.com"
Saves in:saves
Status closed:yes
duplicate:no
migrated:no
wiki:no
Types is:question
is:answer
Exclude -[tag]
-apples
For more details on advanced search visit our help page
Results tagged with
Search options answers only not deleted user 1464

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.

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 …
David Hansen's user avatar
  • 13.1k
12 votes
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 …
David Hansen's user avatar
  • 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 …
David Hansen's user avatar
  • 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 …
David Hansen's user avatar
  • 13.1k
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 …
David Hansen's user avatar
  • 13.1k