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 2666
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.
2
votes
1
answer
744
views
Reference on Casselman-Shalika formula for GL(n) and PGL(n)?
I am looking for reference on Casselman-Shalika formula for GL(n) and PGL(n) at finite place p.
- 105k
0
votes
1
answer
838
views
Euler product of Asai L-function?
Let $\pi$ be an automorphic form of GL(n)/$\mathbb{Q}$ with standard $L$-function
$$L(s,\pi)=\prod_p \prod_{i=1}^n(1-\frac{\alpha_{p,i}}{p^s})^{-1},$$
where $\{\alpha_{p,i}:i=1,\dots,n\}$ are the Sata …
- 3,587
3
votes
0
answers
221
views
Functoriality for triple product GL(2) x GL(2) x GL(2)
Let $f$, $g$ and $h$ be three general automorphic forms on $\operatorname{GL}(2)$.
Do we know that $L(s, f\times g\times h)$ comes from an automorphic form on $\operatorname{GL}(8)$?
4
votes
1
answer
414
views
Fricke involution on GL(3)
Define $\Gamma_0(N)=\{\begin{pmatrix}
a&b&c\\
d&e&f\\
g&h&i
\end{pmatrix}
\in SL(3,\mathbb{Z})|g\equiv h\equiv 0(\mod N)\}$ be the $N$-level congruence subgroup on GL(3).
What should be a Fricke inv …
- 767
6
votes
2
answers
470
views
Symmetric powers of Ramanujan tau-function
Let $\Delta(z)$ be the modular form associated with Ramanujan $\tau$-function.
For any $k=2,3,...$, $Sym^k\Delta$ is conjectured to be an automorphic form on $\mathrm{GL}(k+1)$ and $L(s, Sym^k\Delta) …
- 5,089
4
votes
1
answer
207
views
Local L-function $L(s,\pi_p\times \chi_p)=1$
Let $\pi_p$ be a ramified representation of $GL(n,\mathbb{Q}_p)$.
Let $\chi_p$ be a ramified representation of $GL(1,\mathbb{Q}_p)$.
Is it generally known that
$L(s,\pi_p\times \chi_p)=1$ if $\chi_ …
- 105k
1
vote
0
answers
134
views
Is there an analysis theorem analogous to Kuznetsov/Petersson trace formula?
I am thinking about general differential operator acts on a compact manifold. Is there something similar to Kuznetsov trace formula?
For example, let $f_i $ be the eigenfunctions of an operator $D$, …
- 3,804
9
votes
3
answers
2k
views
Sato-Tate measure for GL(3) Automorphic forms
As we have known, the Sato-Tate measure for GL(2) turned out to be the half circle measure
$\frac{1}{2\pi} \sqrt{4-x^2}dx$ on [-2,2],
which appears in various versions of equi-distribution problems …
- 13.6k
7
votes
2
answers
474
views
Rankin-Selberg integral for GL(3) form with Odd Maass form on GL(2)
Let $F$ be a Hecke-Maass cusp form for $SL_3(\mathbb Z)$.
Let $u$ be a Hecke-Maass cusp form for $SL_2(\mathbb Z)$.
The following integral
$$\mathcal L(s,F\times u)=\int_{{SL}(2,\mathbb{Z})\backslas …
- 8,374
2
votes
0
answers
335
views
Meaning of Ramanujan-Petersson conjecture? [closed]
I found it very hard to explain the Ramanujan-Petersson conjecture in a straightforward way.
I can only say now: think about automorphic forms as sound waves, and then the conjecture predicts that i …
- 3,804
13
votes
1
answer
852
views
What kind of non-cuspidal automorphic representation are not isobaric sums?
Let's say $\pi$ is an automorphic representation on $GL_3(A_{\mathbb Q})$ (or $GL_n(A_{\mathbb Q})$).
If $\pi$ is not cuspidal, what $\pi$ can be other than isobaric sums?
If there is such a thing, …
- 37k
7
votes
1
answer
774
views
Alternative way to prove the functional equation for Eisenstein series?
Let $E(z,s):=\pi^{-s}\Gamma (s) \sum_{(m,n)=1}\frac{y^s}{|mz+n|^{2s}}$ be the real-analytic Eisenstein series.
It satisfies the functional equation $E(z,s)=E(z,1-s)$ with two poles at $s=0,1$.
The m …
- 3,403
10
votes
0
answers
385
views
Residue of Eisenstein Series on GL(n)
Reference: Mœglin, C.; Waldspurger, J.-L.: Le spectre residuel de GL(n)
On GL($n$), the result of Waldspurger shows that if an automorphic representation $\pi$ is non-cuspidal and in the discrete spe …
- 3,804
4
votes
2
answers
1k
views
Any reference on Eisenstein Series for $\Gamma_0(N)$ in $\mathrm{GL}(2)$
What is the best reference on Eisenstein Series for $\Gamma_0(N)$ in $\mathrm{GL}(2,\mathbb{R})$?
For fixed $\Gamma_0(N)$, should there be several Eisenstein series (corresponding to each cusp)?
- 13.6k
4
votes
0
answers
106
views
Examples of conjectural functorial transfer which has $\times GL(1)$ functional equation?
I am look for some conjectural functorial transfer $X$ which
(A)for any $GL(1)$ automorphic representation $\pi$, we have
$L(s, X\times \pi)$ is holomorphic and satisfies certain functional equatio …
- 3,804