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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.
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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
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
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
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
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