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 not deleted
user 6753
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
Meromorphic continuation of Eisenstein series
I'm not familiar enough with the proofs to say if they are more than superficially different, but here is something:
Moeglin-Waldspurger prove continuation crediting Jacquet (see p. xix), instead of …
- 3,183
4
votes
Accepted
Weyl law for SL(2,C)
For general compact manifolds (of dimension $n$), the error term (on the number of eigenvalues less than $T^2$, counted with multiplicity) is $O(T^{n-1})$. So for $\Gamma$ co-compact, the error term i …
- 3,183
0
votes
Automorphic form encoding the orders of $N$ modulo $p$.
The Mellin transform of the Whittaker function of an Eisenstein series on GL(2) (with trivial central character) is
$${L(s+s_1,\chi)L(s+1-s_1,\bar\chi)\over L(2s_1,\chi^2)}$$
where s$_1$ and $\chi$ …
- 3,183
13
votes
1
answer
2k
views
Which Shimura varieties are known to be automorphic?
This seems like something that should be well-known, but as an outsider to the field, I'm having trouble locating precise statements.
Hasse-Weil zeta functions of Shimura varieties should be alternat …
- 3,183
7
votes
1
answer
783
views
What is the support of the Whittaker function of a new vector on GL(2)?
Let $W$ be the normalized Whittaker function associated to a new vector in an irreducible generic representation $\pi$ of $G=GL_2(k)$, where $k$ is a $p$-adic field. Let $c$ be the conductor of $\pi$, …
- 3,183
3
votes
1
answer
412
views
Writing a basis of a representation for $\mathrm{GL}_2(\mathbb Q_p)$ in terms of the new vector
$\DeclareMathOperator\GL{GL}\DeclareMathOperator\res{res}$For an irreducible smooth (generic) representation $\pi$ of $G=\GL_2(k)$ with central character $\omega$, where $k$ is a $p$-adic field, we de …
- 3,183
9
votes
Accepted
classification of irreducible admissible (g,K)-module for GL(3,R)
For a general real reductive group, all irreducible admissible $({\mathfrak g},K)$-modules are quotients of parabolically-induced discrete series (or limits thereof) representations (where we allow " …
- 3,183
14
votes
1
answer
1k
views
Double coset spaces of reductive groups and integral representations of L-functions
Let $G$ be a reductive group over a number field $k$, with center $Z$. Let $P$ be a parabolic subgroup. Let $H$ be a reductive subgroup of $G$. To what extent can we understand the double coset space …
- 3,183
6
votes
Accepted
Different cuspidal automorphic representations with same representations at infinity
This is precisely the content of Harish-Chandra's theorem ("Automorphic forms on Semisimple Lie Groups", LNM 68, 1968), proven for general reductive groups:
Fix a finite-dimensional representation $\ …
- 3,183
7
votes
Where do the real analytic Eisenstein series live?
This is kind of a complicated question, since there isn't really a single good answer.
We begin with a simple Lie group $G$ (for simplicity!). On the one hand, we hopefully have a description of the …
- 3,183
5
votes
Accepted
Reference on Casselman-Shalika formula for GL(n) and PGL(n)?
In this paper, Shintani proves the Casselman-Shalika(-Shintani) formula for GL(n). This preceded Casselman-Shalika's paper by a few years. Several of Cogdell's expository articles on L-functions have …
- 3,183