Search Results
| 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 automorphic-forms
Search options questions only
not deleted
user 38145
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.
3
votes
0
answers
360
views
What is the meaning of the "constant term of Eisenstein series" in terms of Fourier analysis
Let $G$ be a connected, reductive group over $\mathbb Q$, with parabolic subgroup $P = MN$. Let $\pi$ be a cuspidal automorphic representation of $M(\mathbb A)$. For a smooth, right $K$-finite funct …
- 6,180
3
votes
0
answers
79
views
Residual and continuous spectra of $L^2( G(k) \backslash G(\mathbb A) ; \omega)$, and cuspid...
Let $G$ be a connected, reductive group over a number field $k$. Let $\mathbb A$ be the ring of adeles of $k$, $\omega$ be unitary character of $Z_G(\mathbb A)/Z_G(k)$, and $V = L^2(G(k) \backslash G …
- 6,180
9
votes
1
answer
530
views
The space of Whittaker functionals is at most one-dimensional
Let $\mathbf G$ be a connected, reductive group over a local field $F$, and let $(\pi,V)$ be a smooth, irreducible, admissible representation of $G = \mathbf G(F)$. Assume there exists a Borel subgro …
- 6,180
4
votes
1
answer
327
views
Hecke algebra $\mathcal H(\operatorname{GL}_2(\mathbb Q_p)/\operatorname{GL}_2(\mathbb Z_p))...
I was reading James Cogdell's notes here on automorphic representations and came to the following claim about the spherical Hecke algebra $\mathcal H(\operatorname{GL}_2(\mathbb Q_p), \operatorname{GL …
- 6,180
2
votes
2
answers
271
views
Finiteness of the volume of $G(F) \backslash G(\mathbb A)$
Let $G$ be a semisimple algebraic group over a number field $F$ with trivial center. Let $\mathfrak S \subset G(\mathbb A)$ be a Siegel domain (defined in terms of a given maximal split torus and min …
- 6,180
6
votes
2
answers
346
views
Definition of unitary representation of $\mathbf G(\mathbb A_k)$
Let $k$ be a global field, and let $G = \mathbf G(\mathbb A_k)$ for a connected, reductive group $\mathbf G$ over $k$. In these notes by Jayce Getz and Heekyoung Hahn, a unitary representation of $G$ …
- 6,180
6
votes
1
answer
309
views
Making sense out of intertwining operators defined by a vector valued integral
Let $G$ be the rational points of a connected, reductive group over a $p$-adic field $F$. Let $S$ be a maximal split torus of $G$ with $\Delta$ a set of simple roots corresponding to a minimal parabo …
- 6,180
9
votes
1
answer
606
views
The correct determinant exponent of the weight $k$-operator for defining Hecke operators/ade...
For $g \in \operatorname{SL}_2(\mathbb R)$, and $\mathbb H$ the upper half plane, and $k\geq 1$ an integer, the weight $k$-operator on functions $f: \mathbb H \rightarrow \mathbb C$ is defined by
$$ …
- 6,180
2
votes
0
answers
413
views
How can this argument calculating the Haar measure on a parabolic subgroup be generalized to...
Let $\mathbf G$ be a connected, reductive group over a local field $F$. Assume there is a maximal torus $\mathbf T$ which is split over $F$. Let $\mathbf P$ be a parabolic subgroup of $\mathbf G$ co …
- 6,180
4
votes
2
answers
784
views
Reference Request: Definition of Induced Representation for reductive groups over a local field
Let $G$ be a connected, reductive group over a local field $F$ of characteristic zero, and $H$ a closed subgroup of $G$ which is defined over $F$. Let $\mu_H, \mu_G$ be right Haar measures on $H(F), …
- 6,180
6
votes
0
answers
1k
views
Definition of Admissible Representation
Let $G$ be a connected, reductive group over a number field $k$. Let $v$ be a place of $k$.
If $v$ is finite, an admissible representation of $G(k_v)$ is defined to be an abstract representation of $ …
- 6,180
5
votes
0
answers
1k
views
Some questions about cuspidal representations and automorphic representations
My reference is Daniel Bump's book, Automorphic Forms and Representations. $G$ is a connected reductive group over a number field $k$ (in Bump's book he takes $G = \operatorname{GL}_n$). Let $K = K_ …
- 6,180
18
votes
2
answers
1k
views
What is the archimedean Hecke algebra?
Let $\mathbf G$ be a connected, reductive group over $\mathbb Q$. For each nonarchimedean place $v$, let $K_v$ be a maximal compact subgroup of $\mathbf G(\mathbb Q_v)$. The space $\mathscr H(\mathbf …
- 6,180
11
votes
1
answer
692
views
Are the L-functions of a normalized newform and the corresponding cuspidal representation eq...
Let $f \in S_k(\Gamma_0(N))$ be a normalized newform with Fourier expansion
$$f(z) = \sum\limits_{n=1}^{\infty} a_n e^{2\pi i z n}$$
and $a_1 = 1$. Then $f$ is an eigenfunction of all Hecke operato …
- 6,180
10
votes
1
answer
538
views
History of points of view on Eisenstein series
What is the history of Eisenstein series? Did the mathematician Eisenstein actually encounter them?
There are, as far as I know, two major perspectives on what Eisenstein series are. The first is in …
- 6,180