# Questions tagged [automorphic-forms]

Automorphic forms are a generalization of the idea of periodic functions in Euclidean space to general topological groups.

273 questions
Filter by
Sorted by
Tagged with
28 views

### Discreteness of Langland's parameter and its centralizer

Let $G$ be a connected reductive group over a $p$-adic field $F$. Let ${^LG}=\widehat{G}\rtimes \Gamma$ ($\Gamma=\Gamma_F$ the absolute Galois group of $F$) be the L-group of $G$, where $\widehat{G}$ ...
• 1,499
22 views

### If $f$ is $K$-finite, then $Xf$ is also $K$-finite

This problem comes form bump, Automorphic forms and representations, p,300. It's about the ''K-finiteness'' conditions in the definition of the automorphic forms of $GL(2,A)$, where A is the adele ...
• 81
1 vote
39 views

### If $χ_p$ is ramified then $χ(p) = 0$

Consider suppose that $χ_{idelic}$ is the idelic lift of the Dirichlet character $χ$. In my text, it says that if the local character $χ_p$ is ramified that is there exists some u $\in Z_p^{x}$ such ...
23 views

• 81
31 views

• 1,016
1 vote
81 views

### The idempotented algebra

Let $k$ be a field, An idempotented algebra over a field k is a k-algebra H together with a collection E of idempotents of H satisfying the conditions: For all $e_1, e_2 ∈ E$ there exists $e_0 ∈ E$ ...
• 25
87 views

### Complete proof for the shape of quasicharacters of $\mathbb{R}^{\times}, \mathbb{C}^{\times}$

Quasicharacters (:=continuous group homomorphism to $\mathbb{C}^{\times}$) of $\mathbb{R}^{\times}, \mathbb{C}^{\times}$ seems to be known to be following forms (the following is quoted from [Raghuram,...
• 1,016
142 views

### Holomorphic non vanishing modular forms without regularity at infinity

Let $\mathcal{O}(\mathcal{H})^\times$ be the multiplicative group of holomorphic functions on the Poincaré half-plane $\mathcal{H}$ that do not vanish there. Let $j(g,z)=(cz+d)$ and $gz=(az+b)/(cz+d)$ ...
37 views

### Jacquet module of a parabolic induction

Let $G=Sp(2)$ be a symplectic group over a $p$-adic field and $P$ be the Siegel parabolic subgroup of $G$. Let $\text{Ind}_P^G$ be the normalized induction functor from smoothe representations of $P$ ...
• 819
25 views

• 357
60 views

• 1,499
52 views

### Daniel Bump's Automorphic Forms and Representation Exercise 4.7.2 (Page 520)

Exercise 4.7.2 of Daniel Bump's Automorphic Forms and Representations (Page 520) (a) Let $F$ be a local field, either Archimedean or non-Archimedean. By a finite function, we mean a function $\phi$ ...
• 715