Timeline for L and epsilon factors of Gelbart-Jacquet lifts
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 17, 2019 at 14:53 | comment | added | David Loeffler | Agreed, but twisting by a Dirichlet char will change the $\epsilon$-factor. | |
| Sep 17, 2019 at 12:29 | comment | added | Peter Humphries | With that being said, the $L$-function of a self-dual Gelbart-Jacquet lift $\Pi$ whose epsilon factor satisfies $\epsilon(1/2,\Pi) = -1$ trivially vanishes at $s = 1/2$. | |
| Sep 17, 2019 at 9:02 | comment | added | David Loeffler | Certainly it is expected that for any cuspidal auto $\pi$ on $GL(3)$, and any finite set of places $S$, we have $L(\pi, \chi, 1/2) \ne 0$ for all but finitely many finite-order characters $\chi$ unram outside $S$; but I don't think this is known (whether or not $\pi$ is a GJ lift). | |
| Sep 17, 2019 at 7:09 | comment | added | Damon | Thanks a lot for these clarifications. Even if the epsilon factor is nonzero, can we have L-value zero at 1/2? Is that possible for instance for all characters ? | |
| Sep 15, 2019 at 16:32 | comment | added | Peter Humphries | For what it's worth, I've found Gelbart and Jacquet's paper (doi.org/10.24033/asens.1355) quite useful for computing the local epsilon factors and local $L$-functions, given one knows the local data. | |
| Sep 15, 2019 at 15:02 | history | edited | David Loeffler | CC BY-SA 4.0 |
added 205 characters in body
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| Sep 15, 2019 at 14:56 | history | answered | David Loeffler | CC BY-SA 4.0 |