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Results tagged with automorphic-forms
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An automorphic form is a well-behaved function from a topological group $G$ to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup $\Gamma \subset G$ of the topological group. Automorphic forms are a generalization of the idea of periodic functions in Euclidean space to general topological groups.
27
votes
New Geometric Methods in Number Theory and Automorphic Forms
To complement Joel's wonderful and (as far as I understand) very much on point answer, let me quote from the proposal for the parallel program on Geometric Representation Theory, which touches on seve …
- 24.1k
26
votes
What are the local Langlands conjectures nowadays, for connected reductive groups over a $p$...
A brief update: in his amazing talk yesterday at MSRI (available here), Laurent Fargues explained (building on work of Peter Scholze, see his phenomenal talk two weeks ago here and his historic Berkel …
- 24.1k
15
votes
How can I see the relation between shtukas and the Langlands conjecture?
I was hoping someone arithmetically qualified would take this on, but here are some comments from a geometer. One nice perspective I learned from Wei Zhang's ICM address - namely, over function fields …
- 24.1k
10
votes
What are the local Langlands conjectures nowadays, for connected reductive groups over a $p$...
To elaborate on Marty's comment, the simple moral one learns from both the Kazhdan-Lusztig classification of tamely ramified representations and the real local Langlands classification is that L-packe …
- 24.1k
5
votes
Why is Langlands functoriality usually related with period integral in a third group?
I'm not close to familiar enough with the references you cite or examples you ask about to address them, but here's a picture coming out of Sakellaridis and Venkatesh [SV]. Let us label a period not b …
- 24.1k