All Questions
Tagged with geometric-langlands automorphic-forms
6 questions
2
votes
1
answer
164
views
What is the sum operation on torsors induced by Weil uniformization?
Let $k$ be an algebraically closed field, $G$ a reductive group, and $C$ a curve. The algebraic version of the Weil uniformization theorem (see e.g. arXiv:1511.06271v2) says that groupoid of $G$-...
8
votes
0
answers
469
views
Analog of Ramanujan-Petersson conjecture in Geometric Langlands
The Ramanujan conjecture asserts that
\begin{align}
|\tau(p)|\leq 2p^{11/2}
\end{align}
where $\tau(p)$ is the $p^{th}$ Fourier coeffecient in the q-expansion of the weight 12 cusp form $\Delta(z)$. ...
3
votes
1
answer
988
views
Global Langlands function fields
Has V. Lafforgue proved the automorphic-to-Galois direction in the Global Langlands conjectures for general reductive groups over function fields?
What is the current status, more generally?
Related ...
2
votes
1
answer
753
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Reference on Casselman-Shalika formula for GL(n) and PGL(n)?
I am looking for reference on Casselman-Shalika formula for GL(n) and PGL(n) at finite place p.
8
votes
1
answer
2k
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Why is the Arthur trace formula so powerful?
Considering the Arthur trace formula, why are the sort of convolution operators, whose "normalized traces" are given in geometric terms and spectral terms, actually able to distinguish all ...
9
votes
3
answers
1k
views
Why is the simple trace formula a weaker tool than the Arthur trace formula?
What are some concrete examples of theorems which can be deduced from the Arthur trace formula, which do not follow from the simple trace of Kazdhan and Flicker?
(So I do not mean weaker in the sense ...