Timeline for Rankin-Selberg integral for GL(3) form with Odd Maass form on GL(2)
Current License: CC BY-SA 3.0
10 events
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| Sep 19, 2017 at 9:35 | history | edited | Peter Humphries | CC BY-SA 3.0 |
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| Jul 7, 2017 at 15:32 | comment | added | Peter Humphries | That being said, Jack Buttcane has recently been working on understanding these sorts of problems for $\mathrm{GL}_3$ - I would shoot him an email if I were you explaining the exact issue (or just linking this MO question). | |
| Jul 7, 2017 at 15:30 | comment | added | Peter Humphries | @7-adic, replace $u(z)$ with $\Lambda_2 u(z)$, where $\Lambda_2 = 1 + y\left(i\frac{\partial}{\partial x} - \frac{\partial}{\partial y}\right)$ is the weight $2$ raising operator, so that $\Lambda_2 u(z)$ is automorphic of weight $2$. Then you need to replace $F$ with some analogous lowering operator of weight $-2$. Unfortunately little is known about raising and lowering operators for $\mathrm{GL}_3$. | |
| Jul 7, 2017 at 6:44 | comment | added | 7-adic | I am very curious but I don't think $y_2\frac{\partial}{\partial x_2} u(z_2)$ could work. It is not automorphic under $SL_2(\mathbb Z)$ and cannot get passing the "unfolding" technique. | |
| Jul 4, 2017 at 4:25 | history | edited | Peter Humphries | CC BY-SA 3.0 |
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| Jul 4, 2017 at 0:28 | comment | added | Peter Humphries | For what it's worth, a back-of-the-envelope calculation tells me that if you replace $u(z_2)$ with $y_2 \frac{\partial}{\partial x_2} u(z_2)$ and $F$ with $y_1^2 F$, then you should get the correct $L$-function and gamma factors. However, these functions aren't automorphic. | |
| Jul 4, 2017 at 0:11 | history | edited | Peter Humphries | CC BY-SA 3.0 |
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| Jul 3, 2017 at 23:23 | comment | added | Peter Humphries | That's a good question. By "natural" vector, I mean the vector that, when translating from the adèlic language to the classical language, gives you a classical newform. | |
| Jul 3, 2017 at 23:03 | comment | added | 7-adic | Thank you for your great answer! Why are you sure the "natural" vector for $\pi_\infty$ is the spherical one? If that is indeed the case, we only need to find a "natural" vector for $\pi'_\infty$. Since $\pi'_\infty$ is on GL(2), it may not be that hard... | |
| Jul 1, 2017 at 18:05 | history | answered | Peter Humphries | CC BY-SA 3.0 |