Timeline for Modularity of certain theta series associated to hyperbolic lattice
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Feb 21, 2017 at 13:27 | history | edited | Myshkin | CC BY-SA 3.0 |
+ top level tag (nt.)
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| Nov 27, 2016 at 9:04 | answer | added | Philip Engel | timeline score: 1 | |
| Nov 15, 2016 at 19:32 | comment | added | paul garrett | Well, I did not even think carefully whether what you wrote is exactly the right thing, since it is not at all reliably the case that theta lifts are holomorphic automorphic forms. That is, not everything has a "$q$-expansion" of the type popularized in more elementary settings. The nature of the sum looks like a theta lift (with "simple" meaning the colloquial sense), but there are things to check. Pairings to indefinite orthogonal groups do also occur in work of Borcherds. | |
| Nov 15, 2016 at 16:50 | comment | added | Philip Engel | Unfortunately, I don't really have the expertise to understand the papers I found when searching those keywords. By simple function do you mean a sum of step functions or is there another meaning to the word "simple"? Does the theta correspondence produce (mock, quasi, etc) modular forms (functions, etc)? I only care about the coefficients of $q^n$ for $n>0$ so one could modify the above series to sum over all orbits of vectors, or add a Laurent tail. I don't know if that would simplify things. | |
| Nov 14, 2016 at 21:47 | comment | added | paul garrett | This is an image of a simple function on a group $O(n,1)$ under a theta correspondence mapping to $SL(2)$ or possibly a metaplectic group $Mp(2)$ if $n+1$ is odd. Keywords: "theta correspondence", "Howe correspondence", "Segal-Shale-Weil representation", such stuff. | |
| Nov 14, 2016 at 3:33 | history | edited | Philip Engel | CC BY-SA 3.0 |
edited body
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| Nov 14, 2016 at 3:18 | history | asked | Philip Engel | CC BY-SA 3.0 |