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 |
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
$$ …
7
votes
0
answers
289
views
What does it mean for a complex valued function on $G(\mathbb A)$ to be smooth (or smooth of...
Let $\mathbb A$ denote the adeles of $k$, $\mathbb A_f$ the finite adeles, and $k_{\infty} = \prod\limits_{v \mid \infty} k_v$. …
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 $G$ …
5
votes
1
answer
520
views
Sufficient condition for the absolute convergence of Fourier series of a function on the ade...
What about when $G = \mathbb A_k/k$ for $k$ a number field, and $\mathbb A_k$ the adeles of $k$? …
5
votes
1
answer
222
views
Do we have $G(\mathbb A_S) G(k) = G(\mathbb A)$ for sufficiently large $S$?
Let $\mathbb A$ be the ring of adeles of $k$, and $\mathbb A_S = \prod\limits_{v \in S} k_v \prod\limits_{v \not\in S} \mathcal O_v$ for any (large) finite set of places $S$ containing the archimedean …
2
votes
0
answers
300
views
Question about the Fourier expansion of adelic Eisenstein series for $\operatorname{GL}_2$
My reference is Daniel Bump's book, Automorphic Forms and Representations, Chapter 3.7. Let $k$ be a number field, $G = \operatorname{GL}_2$, $B$ and $T$ the usual Borel subgroup and maximal torus o …
2
votes
2
answers
208
views
Definition of cusp form in $L^2$ and convergence over $N_{\mathbb Q} \backslash N_{\mathbb A}$
Let $G$ be an adjoint semisimple group over $\mathbb Q$ with parabolic subgroup $P = MN$ in good position relative to a compact subgroup $U= \prod\limits_v K_v$ of $G(\mathbb A)$. Let $L$ be the spac …
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 …
1
vote
0
answers
166
views
Absolute convergence of the Fourier series of a smooth adelic function
Let $f: \mathbb A/\mathbb Q \rightarrow \mathbb C$ be a smooth function. Smooth means that $f$ is continuous, smooth in the archimedean argument, for every $(x_0,y_0) \in \mathbb A = \mathbb R \time …
1
vote
0
answers
87
views
$H(\mathbb A)^0/H(k)$ is homeomorphic to a closed set in $G(\mathbb A)/G(k)$
The setting is $k$ is a number field, $\mathbb A$ is the ring of adeles of $k$, $H$ is a closed subgroup of an algebraic group $G$, both defined over $k$, and $H(\mathbb A)^0$ is the subgroup of $h \in …
1
vote
0
answers
91
views
The kernel $K(x,y)$ as an integral over Eisenstein series for $\operatorname{GL}_2$
Let $G = \operatorname{GL}_2$, $f \in C_c^{\infty}(G(\mathbb A)/Z(\mathbb A))$, and $V = L^2( G(\mathbb Q)Z(\mathbb A)\backslash G(\mathbb A))$ (trivial central character). Then the operator $R(f)$ o …