Timeline for Voronoï summation for cusp forms with characters
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 24, 2022 at 19:21 | answer | added | Subhajit Jana | timeline score: 1 | |
| Nov 21, 2022 at 14:20 | comment | added | user50139 | @SubhajitJana can you please give more details? I am not familiar with the Kirillov model, and knowing how to obtain such a bound could be extremely helpful to me. | |
| Nov 19, 2022 at 20:40 | comment | added | Subhajit Jana | You usually expect square-root cancellation, that is, the expected bound is $\ll_{q,\epsilon} B^{1/2+\epsilon}$ with polynomial dependency in $q$ which follows from some Voronoi formula. In this particular case, using the Kirillov model one can show the sum is $O(\sqrt{B})$ uniformly in $q$. | |
| Nov 18, 2022 at 19:27 | comment | added | user50139 | @Kimball I guess :) | |
| Nov 18, 2022 at 19:27 | comment | added | user50139 | @SubhajitJana, on a first approximation you may think of $h(x)=f(x/B)$ where $f$ is a fixed compactly supported function and $B$ is some parameter tending to infinity, so upper bounds should depend on $B$. Here $\chi$ is fixed, and so is $N$ (the cusp form itself is fixed) but $q$ is varying. | |
| Nov 18, 2022 at 19:22 | comment | added | user50139 | @m34 At a first glance it seems to be the sort of thing I want, yes, thank you very much! Other remarks are still welcome, of course :) | |
| Nov 18, 2022 at 9:48 | comment | added | Subhajit Jana | What is the support of $h$ here? Is $h$ a fixed test function? Then the sum is trivially $O(1)$. Also, you need to specify which parameters ($\pi$, $N$, $q$, $C(\chi)$, etc.) are fixed and which are varying. | |
| Nov 18, 2022 at 6:07 | comment | added | Kimball | In an attempt to solve an unrelated problem, I was led to... - Doesn't that mean it's not unrelated? | |
| Nov 17, 2022 at 18:18 | comment | added | Alex M. | That lemma equates the sum that the OP is studying to an even more complicated expression involving three sums and an integral. In particular, it gives no upper bound for the OP's sum. | |
| Nov 17, 2022 at 17:33 | comment | added | m34 | Does Lemma 2.4 of arxiv.org/pdf/1707.01576.pdf do what you need? | |
| Nov 17, 2022 at 17:16 | history | asked | user50139 | CC BY-SA 4.0 |