Timeline for Shortest/Most elegant proof for $L(1,\chi)\neq 0$
Current License: CC BY-SA 3.0
25 events
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| Apr 4, 2021 at 22:29 | answer | added | reuns | timeline score: 4 | |
| Jun 30, 2018 at 15:42 | answer | added | C.S. | timeline score: 2 | |
| May 4, 2016 at 22:44 | history | edited | Gerry Myerson |
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| May 4, 2016 at 21:49 | history | edited | José Hdz. Stgo. | CC BY-SA 3.0 |
added 2 characters in body
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| Jan 25, 2015 at 12:37 | answer | added | Sylvain JULIEN | timeline score: 0 | |
| Jan 25, 2015 at 0:38 | history | edited | GH from MO |
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| Jan 25, 2015 at 0:29 | comment | added | paul garrett | In terms of "clearest causation", I still do think that the spectral argument using the constant term of Eisenstein series for $GL_2$ is the most memorable, the most explanatory, and the most suggestive of the broader situation... | |
| Jan 24, 2015 at 23:16 | answer | added | Vesselin Dimitrov | timeline score: 11 | |
| Sep 25, 2010 at 18:23 | answer | added | Franz Lemmermeyer | timeline score: 25 | |
| Jun 24, 2010 at 22:00 | answer | added | Terry Tao | timeline score: 29 | |
| May 27, 2010 at 3:11 | answer | added | Peter Humphries | timeline score: 11 | |
| May 26, 2010 at 21:01 | vote | accept | M.G. | ||
| May 25, 2010 at 5:56 | answer | added | Pierre-Yves Gaillard | timeline score: 2 | |
| May 25, 2010 at 5:52 | comment | added | Junkie | Also, this is longer not shorter, but the use of Eisenstein series to prove non-vanishing on the 1-line was in vogue (originally Jacquet-Shalika in the 70s springerlink.com/index/H626367320663544.pdf ), due to Sarnak's reworking a few years ago. See math.huji.ac.il/~erezla/papers/steverevised.pdf (and the Sarnak ref of there), which does a zero-free region. The proof that symmetric square $L$-functions don't vanish at the edge, and indeed lack Siegel zeros (unless induced) by Goldfeld, Hoffstein, Lieman followed the product idea. jstor.org/stable/2118544 | |
| May 25, 2010 at 5:03 | comment | added | Junkie | As for (1), I think it is a bad idea. There is a fundamental distinction between the two cases. The idea is, that if $L(1,\chi)=0$ for $\chi$ complex, then so does its conjugate, which gives a double zero in the product that David Speyer gives below. Enlarging this idea, we get a fairly decent zero-free region for $L(1,\chi)=0$ for $\chi$ complex (I don't recall, but $1/\log D$ maybe). But for real characters this is not true, and we have to worry about the so-called Siegel zeros, and the zero-free region is much worse (as $1/\sqrt D$). The difference is the single vs double effect. | |
| May 24, 2010 at 23:50 | answer | added | Wadim Zudilin | timeline score: 9 | |
| May 24, 2010 at 23:37 | answer | added | David Hansen | timeline score: 5 | |
| May 24, 2010 at 23:27 | answer | added | Brad Rodgers | timeline score: 7 | |
| May 24, 2010 at 22:49 | answer | added | José Hdz. Stgo. | timeline score: 6 | |
| May 24, 2010 at 20:49 | answer | added | David E Speyer | timeline score: 26 | |
| May 24, 2010 at 20:25 | answer | added | KConrad | timeline score: 11 | |
| May 24, 2010 at 19:58 | answer | added | Mark Lewko | timeline score: 7 | |
| May 24, 2010 at 19:53 | answer | added | Robin Chapman | timeline score: 34 | |
| May 24, 2010 at 19:50 | answer | added | Pete L. Clark | timeline score: 16 | |
| May 24, 2010 at 19:39 | history | asked | M.G. | CC BY-SA 2.5 |