Timeline for Which values of symmetric square $L$-functions are critical?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 8, 2015 at 17:52 | vote | accept | David Loeffler | ||
| Sep 8, 2015 at 15:28 | answer | added | François Brunault | timeline score: 3 | |
| Sep 8, 2015 at 10:18 | comment | added | David Loeffler | No, for Hida $\chi$ is an arbitrary Dirichlet character; I'm taking $\chi = 1$ in his notation. The point is that Hida's definition of $D_\ell(X)$ has a factor of $\psi'\psi_P(\ell)^{-1}$ which is not there in my definition (where $\psi' \psi_P$ is Hida's notation for the nebentypus of $f$). | |
| Sep 8, 2015 at 10:15 | comment | added | kantelope | Reading Hida, is there any link between $\chi$ at the top of page 96 and anything previous? You seem to interpret it as the character of the form, but I do not see this explicitly. | |
| Sep 8, 2015 at 9:50 | comment | added | David Loeffler | Magma agrees with me and disagrees with Hida, then. (Magma only seems to give critical values in the right half of the $s$-plane, which is weird; I can't find any description of the CriticalPoints function in the Magma docs, so it's not clear if this is intended behaviour or a bug.) | |
| Sep 8, 2015 at 9:47 | comment | added | kantelope | Magma claims (I know not how) that for $k=5$, the critical points are 6,8, and when I twist it by some character $\epsilon_f^{-1}$ who has $\epsilon(-1)=-1$, then they become 5,7. | |
| Sep 8, 2015 at 9:34 | comment | added | David Loeffler | For $k$ even there is no difference between Hida's statement and my computations. The issue is only for $k$ odd. | |
| Sep 8, 2015 at 9:33 | comment | added | kantelope | What is the answer for $k=2$? Here $s=2$ is critical. | |
| Sep 8, 2015 at 9:24 | history | asked | David Loeffler | CC BY-SA 3.0 |