Search Results

$R$ is a 2-dimensional conductor 133 representation of the absolute Galois group of the rationals into $GL(2,\mathbf{C})$, whose associated representation to $PGL(2,\mathbf{C})$ cuts out the $A_4$ ext …

I will offer some words on this, but only because no-one else has; I was holding out hoping that one of the more automorphic people would chip in. It might be worth taking much of the below with a pin …

Minhyong's comments indicate the issue here. If I want to come up with an extension unramified outside $p$ then why not look at the 2-dimensional mod $p$ representation attached to the $\Delta$ functi …

For what it's worth I can now answer Q0. I believe it is not true in general that $\pi_v$ and $\pi'_v$ will have to have the same central character. We can let $G$ be a torus $T$. If $S$ is a finite s …

Your assumption as written is not quite correct. The irreducible $n$-dimensional irreducible representations of the Langlands group should correspond I think to all cuspidal automorphic representation …

I have accepted Junkie's answer to this question. But on analysing his working program and comparing it with my program-that-didn't-work I could easily find the bug in my program: I erroneously though …

Is this really a sensible question to ask, I wonder? Here's a guess as to what the answer might look like. The Weil-Deligne group comes in three pieces. First there's inertia. Then there's a copy of …

Surprisingly, the case of modular curves is misleading! General theory of correspondences, plus the theory of the mod $p$ reduction of curves like $X_0(Np)$ ($p$ doesn't divide $N$) give a relationshi …

@Junkie: here are the first 100 coefficients according to my computer program that doesn't work: [1, 0.3090 + 0.9511*I, -0.5000 + 1.539*I, 0, 0, -1.618, 0, 0.8090 + 0.5878*I, -1.309 - 0.9511*I, 0, 1. …

There are all sorts of problems with the Langlands conjectures that we (as far as I know) have no idea at all how to approach. As a very simple example of an issue for $GL(2)$ over $\mathbf{Q}$ that w …