# Tagged Questions

**4**

votes

**1**answer

181 views

### looking for reference on dihedral, tetrahedral, or octahedral forms

I am looking for a reference on dihedral, tetrahedral, or octahedral forms. As far as I read, they are some cuspidal automorphic forms on $GL(2)$ induced from $GL(1)$. Dihedral is from $GL(1)/K$ to ...

**10**

votes

**2**answers

350 views

### Langlands' original observation about Ramanujan conjecture

Obviously functoriality of arbitrary high symmetric power lifts of automorphic forms on GL(2) will lead to the Ramanujan conjecture. But I guess that is too strong for Ramanujan. I came across some ...

**7**

votes

**1**answer

175 views

### standard zero free region of automorphic L-function on GL(N)

Let $L(s,\pi)$ be the standard(Godement-Jacquet) $L$-function of $\pi$, where $\pi$ is a cuspidal automorphic represetation of $GL(m,A_Q)$.
What's the standard zero-free region for $L(s,\pi)$? any ...

**0**

votes

**1**answer

157 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 ...

**3**

votes

**0**answers

80 views

### Functoriality for triple product GL(2) x GL(2) x GL(2)

Let $f$, $g$ and $h$ be three general automorphic forms on GL(2).
Do we know that $L(s, f\times g\times h)$ comes from an automorphic form on GL(8)?

**2**

votes

**0**answers

132 views

### Conceptual reason behind Shimura lifts

Shimura lifts are correspondence between integer weight and half-integral weight automorphic forms. Half integral weight things are associated to representation of a double cover of $G ...

**13**

votes

**5**answers

2k views

### What is the “reason” for modularity results?

The question is a little wishy-washy, but I take my cues from other popular questions that relate to the philosophy behind the mathematics as Why do Groups and Abelian Groups feel so different? .
I ...

**2**

votes

**2**answers

561 views

### Are the $L$-functions of $X_0(N)$ automorphic?

This question, like all of my previous questions regarding Langlands, is very naive.
All $g\geq 1$ curves come from quotients of the upper half plane. The curves $X_0(N)$ come from quotients of ...