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At least it should be true under suitable assumptions. Jacquet-Shalika proved nonvanishing of automorphic $L$-functions of unitary cuspidal representations of GL($m$) at $s=1$. An automorphic $L$-f …

Let me give at least a partial answer. If you want to view the 1 and 2 dimensional theories uniformly, you should look at everything adelically. In dimension 1, Dirichlet characters can be viewed as …

Sort of. You are asking about a (generalized local) Jacquet-Langlands correspondence. Roughly what this says is that there is a correspondence between discrete series representations of $G$ and $G'$ …

I don't know an explicit reference for you, but I can tell you how these things are done and point you to some related reference. These groups are closely related to general linear groups via acciden …

For the first question, it is only true that if $D$ is a (totally) definite quaternion algebra over a number field $K$, then the weight 0 automorphic forms factor through a finite set (1-sided ideal c …

If I understand correctly what you are looking for, then yes, a fair amount of work has been done. Deitmar and Hoffman use a simple trace formula on SL(3) to get asymptotics of class number of cubic …

I must have missed this question a month ago, but hopefully you're still interested. I haven't read that particular paper, but simple trace formulas have restricted test functions, which for one can …

I think the confusion here lies in what is being called reciprocity (and perhaps the interpretation of "simple"). If by Langlands reciprocity, you mean a correspondence between classical Artin repres …

Prasad and Ramakrishnan (arXiv link) study how the signs of (discrete series) representations behave along the local Langlands correspondence, not just for GL($n$), but for all inner forms. Assume th …

The classical setting of modularity is that one can associate elliptic modular forms (or automorphic representations of GL(2)/$\mathbb Q$) to elliptic curves over $\mathbb Q$. This has far-reaching c …

A lot is known--too much to try to summarize--and I think this philosophy came about after seeing numerous examples, beginning with Harder-Langlands-Rapoport (base change for GL(2)), and thinking abou …

Arthur's long-awaited book project is now published (The endoscopic classification of representations: orthogonal and symplectic groups). However, in the book he takes some things for granted: The …

Updated answer (Oct 2024): While Arthur did not finish some preprints referred to in his book ([A24]-[A27]), [A24] was dealt with by Moeglin and Waldspurger, and this arXiv preprint which was just pos …