Timeline for Automorphic forms annihilated by $I_1$ but not $I_2$ for finite codim ideals $I_1 \subsetneq I_2$
Current License: CC BY-SA 3.0
4 events
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| Jul 22, 2016 at 16:27 | comment | added | paul garrett | First, if you allow Eisenstein series of minimal parabolics, taking derivatives gives a lot of different ideals. E.g., for $GL_n$ the Harish-Chandra isom is easy to understand. No global constraints, just local. If you constrain growth, this tends to discretize things, but apart from Arthur/Selberg type conjectures, I don't think we know what can appear as cuspidal spectrum, for example. | |
| Jul 22, 2016 at 15:50 | comment | added | Dan | @paulgarrett: Thanks for your response! Is there a way to begin with a finite codim ideal $I$ in $\mathcal{Z}$ and construct an Eisenstein series annihilated by $I$? I'm mostly interested in whether or not a characterization of the annihilators of automorphic forms exists that distinguishes them in the finite codimensional ideals of $\mathcal{Z}$, and (better yet!) characterizations that allow for distinguishing annihilators of automorphic forms of a fixed growth rate. | |
| Jul 22, 2016 at 14:58 | comment | added | paul garrett | If a given automorphic form has a continuous parameter, e.g., is an Eisenstein series (possibly with cuspidal data, etc.), its derivative with repect to that continuous parameter is only annihilated by a strictly higher power of the ideal annihilating the original. This is very easy, and/but probably exactly what you don't want to consider... ? | |
| Jul 22, 2016 at 14:17 | history | asked | Dan | CC BY-SA 3.0 |