Timeline for Meromorphic continuation of Eisenstein series
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
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| Mar 19, 2011 at 19:46 | comment | added | Alexander Braverman | I am actually trying to deal with affine Kac-Moody groups. | |
| Mar 18, 2011 at 4:50 | comment | added | B R | You mentioned the other "critical component", of course :) Your comment seems to imply that you are interested in continuing not-necessarily-cuspidal-data Eisenstein series (maybe even non-${\mathfrak z}(g)$-finite?). I think that would be an MO-worthy question in itself. I wouldn't have much coherent to add to that discussion, but maybe someone else would. | |
| Mar 18, 2011 at 2:16 | comment | added | Alexander Braverman | Also I tried to read Selberg's original proof in his ICM paper and didn't understand it. I think that Sarnak couldn't understand it either and he rewrote it a little (using slightly different idea). Selberg's original proof remains a mystery for me. | |
| Mar 18, 2011 at 2:15 | comment | added | Alexander Braverman | Actually, in the situation I have to deal with, the "critical component" of Bernstein's proof turns out to be the property that in some domain the system has unique solution. In any case, Moeglin-Waldspurger prove more than Bernstein - they give you some information about poles which Bernstein's proof has no chance to give. Thank you all very much! | |
| Mar 17, 2011 at 17:33 | comment | added | B R | Also, it's not clear to me that these proofs don't implicitly prove the critical component needed to invoke Bernstein's continuation principle (that the parametrized system of equations has a locally finite-dimensional solution space). | |
| Mar 17, 2011 at 8:10 | comment | added | B R | Looking around a bit more, Jacquet attributes Moeglin-Waldspurger's proof to Colin de Verdière, so that may be our answer. Thanks for the working link! | |
| Mar 17, 2011 at 8:08 | history | edited | B R | CC BY-SA 2.5 |
added 58 characters in body
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| Mar 17, 2011 at 5:43 | comment | added | Denis Chaperon de Lauzières | The proof of Colin de Verdière is indeed very nice, and it would be very interesting to see how far it can generalize (it is written for subgroups of $SL_2(\mathbf{R})$ with a single cusp; the paper is available numdam.org/numdam-bin/fitem?id=AIF_1983__33_2_87_0 on Numdam.) | |
| Mar 16, 2011 at 23:05 | history | answered | B R | CC BY-SA 2.5 |