Timeline for Primer on Eisenstein series
Current License: CC BY-SA 4.0
10 events
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| Jul 27, 2019 at 0:05 | history | edited | paul garrett | CC BY-SA 4.0 |
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| May 16, 2016 at 12:51 | comment | added | paul garrett | @DavidFeldman, those lectures are rather sketchy, I think. Perhaps others are better able to fill in all the details than am I. | |
| May 16, 2016 at 5:14 | comment | added | David Feldman | >As I have noted elsewhere, Bernstein's ideas about meromorphic continuation of Eisenstein series are not well-documented, or, perhaps, not documented. Do the five lectures linked here count? math.uchicago.edu/~mitya/langlands.html | |
| May 15, 2016 at 4:18 | history | edited | David Feldman | CC BY-SA 3.0 |
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| Aug 25, 2015 at 13:12 | comment | added | paul garrett | ... [cont'd] is the trick (one way or another) of identifying (self-adjoint) compact operators in a "spectral decomposition", to use the discreteness of their spectrum. Y. Colin de Verdiere used the (Lax-Phillips/Faddeev-Pavlov) discrete decomposition of spaces of pseudo-cuspforms to prove meromorphic continuation of genuine Eisenstein series, by observing that after an elementary modification, they satisfy a differential equation whose resolvent is compact... For example, at math.umn.edu/~garrett/m/v/cdv_eis.pdf there is an explication of the latter. | |
| Aug 25, 2015 at 13:06 | comment | added | paul garrett | The "rigidity" is the Mostow-Margulis-etal theorems that assert that most co-finite-volume discrete subgroups of semi-simple real Lie groups are "arithmetic". Further, the "congruence subgroup problem"'s positive resolution for essentially all higher-rank groups is that mostly these discrete groups are "of congruence type", so p-adic and adelic ideas are relevant. Langlands was trying to preserve some generalities that turned out not to exist, to some degree. The "discretization"... [cont'd] | |
| Aug 25, 2015 at 10:27 | comment | added | Spencer Leslie | Sorry to resurrect an older answer, but I was thinking on the answer this morning, and wondering if you could elaborate on 1) the rigidity theorems you reference in the first paragraph and their relevance, and 2) the discretization arguments mentioned towards the end. No exposition or article I have read on Eisenstein series have mentioned such topics, and I am afraid I don't know to what you are referring. | |
| May 9, 2015 at 14:36 | vote | accept | Spencer Leslie | ||
| May 8, 2015 at 0:23 | comment | added | paul garrett | I hasten to comment that E. Lapid has written many wise notes about Eisenstein series... and has noted some crazy subtleties... but/and there is no trivial resolution/outcome. | |
| May 8, 2015 at 0:10 | history | answered | paul garrett | CC BY-SA 3.0 |