All Questions
14 questions with no upvoted or accepted answers
13
votes
0
answers
523
views
Euler Subgroups and Automorphic L-functions
Recently, I have read about the Whittaker expansion for $\mathrm{GL}_n$ and was struck by the utility of the mirabolic subgroup, $\mathrm{P}_n\subset \mathrm{GL}_n$ of matrices with bottom row $(0\; 0 ...
- 2,516
9
votes
0
answers
230
views
Clozel's unpublished manuscript
I'm looking for Clozel's unpublished manuscript
L. Clozel, Modular properties of automorphic representations I: Applications of
the Selberg trace formula (1993)
cited in Urban's Eigenvarieties ...
- 3,799
8
votes
0
answers
481
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 \...
- 5,424
8
votes
0
answers
335
views
Irreducibility of Galois representations attached to unitary groups
If $G$ is a unitary group in $n$ variables over $\mathbb Q$, attached to an hermitian form for an imaginary quadratic extension $E/\mathbb Q$ and if we suppose that the hermitian form is definite over ...
- 26k
5
votes
0
answers
156
views
Reference Request: Completeness of the space of all Whittaker models(a lemma in JPSS1981)
$\DeclareMathOperator\GL{GL}$There is a lemma in the proofs of local converse theorem stated as
Suppose $F$ is a non-archimedean local field, $\psi$ is a non-trivial addtive character on $F$. $N_n$ ...
- 53
5
votes
0
answers
359
views
Examples of Rankin-Selberg L-functions from Eisenstein series
I've been digging for awhile to not much success, so I figure I would try here:
I am looking for some references which compute explicitly examples of Rankin-Selberg L-functions from the constant ...
- 3,799
3
votes
0
answers
148
views
Casimir eigenvalues of p-adic automorphic representations
In the context of p-adic local Langlands correspondence:
Is it possible to define Casimir eigenvalues for p-adic automorphic representations? If a local representation arises from a global Galois ...
- 2,907
3
votes
0
answers
117
views
Reference Request: Local decomposition of GGP period integrals of cuspidal forms on unitary groups
Setup: Let $E/F$ be a CM-extension of global number fields. Let $(V,\phi)$ be an Hermitian space of dimension $n$ over $E$. Let $(V^{\flat}, \phi^{\flat})$ be a subspace of $V$ of dimension $n-1$ on ...
- 639
3
votes
0
answers
164
views
Using the Hilbert symbol to find nice field extensions
Let $p$ and $q$ be (not necessarily distinct) odd primes and let $F=\mathbb{Q}_p(\mu_q)$. The $q^{th}$ Hilbert symbol induces a non-degenerate alternating form $$(\cdot,\cdot)_q:F^\times/(F^\times)^q\...
- 2,516
3
votes
0
answers
162
views
Hecke eigensystem in cohomology vs. compactly supported cohomology
What follows is a question that's probably well-known to experts, but I haven't been able to find a reference.
Let $\mathrm G$ be a connected, semisimple $\mathbb Q$-group. Let $K \subset \mathrm G(\...
- 391
3
votes
0
answers
163
views
Oscillatory integral moments of $L(\frac{1}{2} + it, f \times f)$
Understanding moments and subconvexity bounds for $L$-functions is a big topic with a lot of activity. I'm currently looking at a related problem, bounding
$$
\int_0^T L\left(\tfrac{1}{2} + it, f \...
- 1,570
3
votes
0
answers
293
views
multiplicity of automorphic representation of unitary similitude group
Let $G$ be a unitary similitude group over $\mathbb{Q}$ (as in the book of Harris-Taylor), $\pi$ an irreducible automorphic representation of $G(\mathbb{A})$. I'm looking for some results on its ...
- 66
2
votes
0
answers
100
views
Function equation over general number fields
Let $\chi$ be a Hecke character on a number field $k$, where could I find a precise reference for the function equation of the $GL(1)$ L-functions
$$L(s, \chi)?$$
I only find references for the case ...
- 927
2
votes
0
answers
159
views
The dimension of the space of automorphic forms with multiplier system
Let $\Gamma$ be a discrete subgroup of $SL_{2}(\mathbb{Z})$ and $\vartheta$ a multiplier system of weight $k$ for $\Gamma$, by which we mean a function $\vartheta:\Gamma \rightarrow \mathbb{C}$ ...
- 433