Timeline for Maximum value of newform from Galois representation
Current License: CC BY-SA 4.0
13 events
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| Apr 13, 2021 at 6:00 | comment | added | GH from MO | @reuns: Perhaps you should ask the OP about what he/she means. | |
| Apr 12, 2021 at 23:07 | comment | added | reuns | @GHfromMO Does the OP mean an approximate value for the maximum? If so then the key should be to find the level from the ramification. | |
| Apr 12, 2021 at 17:05 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Apr 12, 2021 at 16:43 | comment | added | GH from MO | I added the adjective "holomorphic" to the post. Note that there are Maass forms of all weights on the upper half-plane, including those that do not come from holomorphic cusp forms (cf. Henri Cohen's remark). | |
| Apr 12, 2021 at 16:42 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Apr 12, 2021 at 16:40 | comment | added | GH from MO | @HenriCohen: In the sup-norm problem for holomorphic cusp forms, one studies $y^{k/2}|f(x+iy)|$, as you suggest. I am sure the OP had this function in mind (and so did I). | |
| Apr 12, 2021 at 16:33 | comment | added | Henri Cohen | I am not sure I understand the question: isn't a holomorphic modular form (cuspidal or not) unbounded on the upper half-plane ? It is y^{k/2}|f(x+iy)| which is bounded. | |
| Apr 12, 2021 at 15:46 | history | edited | sup |
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| Apr 12, 2021 at 15:45 | comment | added | sup | I had holomorphic modular forms in mind. | |
| Apr 12, 2021 at 13:45 | comment | added | GH from MO | I think you can only attach a Galois-representation to cohomological cuspidal automorphic reprepresentations (and their newforms). The maximum value of a newform is a subtle problem, even for holomorphic newforms on the upper half-plane, and I don't know of any connection with Galois-representations. | |
| Apr 12, 2021 at 13:16 | history | edited | sup |
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| Apr 12, 2021 at 10:10 | review | First posts | |||
| Apr 12, 2021 at 10:36 | |||||
| Apr 12, 2021 at 10:08 | history | asked | sup | CC BY-SA 4.0 |