Timeline for Modular forms with finitely many or very few non-zero Fourier coefficients
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Apr 25, 2021 at 15:41 | comment | added | GH from MO | @FrançoisBrunault: Thanks for your valuable comment! | |
| Apr 25, 2021 at 15:06 | comment | added | François Brunault | Just to clarify: Serre's non-lacunarity result (Théorème 17) applies to all modular forms, not just newforms. | |
| Apr 25, 2021 at 10:01 | vote | accept | Alphonse | ||
| Apr 25, 2021 at 9:50 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Apr 25, 2021 at 8:57 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Apr 25, 2021 at 8:48 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Apr 25, 2021 at 8:47 | comment | added | GH from MO | @Alphonse: Those products don't have positive density. The number of such integers up to $x$ is asymptotically a constant times $x/\sqrt{\log x}$, as proved by Landau. | |
| Apr 25, 2021 at 8:45 | comment | added | Alphonse | Thanks for your nice answer. I'm not sure about the CM case: do you mean that the set of $n$ such that the prime factors of $n$ split in the quadratic number field associated with $f$ has density 0? Doesn't the set of products $p_{i_1} \cdots p_{i_k}$ (where each $p_j$ splits) have positive density? | |
| Apr 25, 2021 at 8:25 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Apr 25, 2021 at 8:19 | history | undeleted | GH from MO | ||
| Apr 25, 2021 at 8:19 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Apr 25, 2021 at 8:07 | history | deleted | GH from MO | via Vote | |
| Apr 25, 2021 at 8:06 | history | answered | GH from MO | CC BY-SA 4.0 |