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 43737
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.
8
votes
1
answer
315
views
Average bounds on Rankin-Selberg coefficients for modular forms
Let $f$ be a cuspidal Hecke newform of weight $k$ and level $N$, and denote by $a_f(n)$ its $n$-th Fourier coefficient. The newform $f$ is normalized so that $a_f(1) = 1$. As a consequence of Rankin-S …
- 5,424
6
votes
1
answer
212
views
What is the conductor of an automorphic representation for $\Gamma_0(q)$ in $GSp(4)$?
Let $\pi$ be a generic cuspidal automorphic representation on $GSp(4)$, with level $\Gamma_0(q)$ (the group of symplectic matrices with lower left block divisible by $q$), i.e.
$$\Gamma_0(q) = \left\{ …
- 5,424
9
votes
0
answers
210
views
Why and how is a representation "continuously decomposable"?
What I am asking may apply to a much more general setting and I am interested in the underlying level of generality of these statements, mostly with canonical references. However I state the question …
- 5,424
8
votes
0
answers
450
views
Formal degree of discrete series representations
Let $G$ be a locally compact unimodular group. A continuous irreducible unitary representation $\pi$ of $G$ is said to be a discrete series if its matrix coefficients (defined by $\xi^\pi_{v,w} : g \m …
- 5,424
9
votes
1
answer
375
views
Relation between $\xi$-cohomological and discrete series
Sometimes, results on automorphic representations are available only under local assumptions. Typically, one could require the representation to be a $\xi$-cohomological cuspidal representation, and I …
- 5,424
14
votes
1
answer
522
views
Bound for $GL(3)$ symmetric square
Let $\pi$ be an automorphic representation of $GL(3)$ over a number field. Let $a_n$ be the coefficients of $L(s, \pi, \mathrm{sym}^2)$. Do we know if
$$\sum_{n>0} \frac{|a_n|}{n^s}$$
and
$$\sum_{n>0} …
- 5,424
7
votes
0
answers
135
views
Computing explicit matrix coefficients
I would like to understand in a more explicit way the Fell topology on unitary duals, that is to say the convergence of matrix coefficients of local representations.
If I consider a local representati …
- 5,424
8
votes
1
answer
461
views
Equivalence between Ramanujan and Selberg conjectures
At first the Ramanujan conjecture for automorphic forms and the Selberg conjecture appear to be understood as totally independent. However, they are now known to be tighyly connected once viewed in th …
- 5,424
3
votes
2
answers
245
views
Compactness of the automorphic quotient and genericity
Let $G$ be a reductive group defined over a field $F$. Let $\mathbf{A}$ denote the ring of adeles of $F$. My question is:
Assuming the automorphic quotient $[G]=G(F) \backslash G(\mathbf{A})$ is c …
- 5,424
8
votes
1
answer
523
views
How strong is the requirement of being a Gelbart-Jacquet lift?
Let $\pi$ be a cuspidal automorphic representation of $\mathrm{GL}(3)$ over a number field $F$. I am wondering how general are Gelbart-Jacquet lifts of automorphic representations of $\mathrm{GL}(2)$ …
- 5,424
11
votes
2
answers
1k
views
Relation between Fourier coefficients and Satake parameters
Let $L(s)$ be an automorphic L-function (attached to a self contragredient automorphic representation on $GL(3)$), according to the following notations for $s$ of sufficiently large real part:
$$L(s) …
- 5,424
19
votes
1
answer
908
views
What computer program for automorphic forms
This question has its origins in this entertaining discussion on MO.
There are many programs (CAS) and libraries that are able to handle algebraic expressions. These are both a verification tool for …
- 5,424
6
votes
1
answer
185
views
Fields of rationality as a notion of automorphic size
I want to interpret the degree of the field of rationality of an automorphic form as a notion of size, analogously to the conductor, and this question is about the possible obstructions to do so. The …
- 5,424
2
votes
0
answers
81
views
Continuity of the conductor of automorphic representations
I am interested in properties of (semi-)continuity of the conductor of automorphic representation. Let $F$ be a number field.
The meta question is, given a function on the unitary dual of $PGL(2, F)$ …
- 5,424
4
votes
1
answer
223
views
Are all these representations supercuspidal
Let $D$ a division quaternion algebra over a number field $F$, and consider $(V,q)$ be a $D$-hermitian space of $D$-dimension $2$, and introduce its group of isometries
\begin{align*}
\mathrm{GU}(V, q …
- 5,424