Timeline for Equidistribution of $\{\alpha p\}$ for $p$ in an arithmetic progression
Current License: CC BY-SA 4.0
11 events
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| Sep 14, 2020 at 18:31 | comment | added | GH from MO | @DanielLoughran: The previous comment (by Captain Darling) was meant for you. | |
| Sep 14, 2020 at 16:53 | comment | added | Dr. Pi | It is not difficult to extend Vinogradov's approach to $K/\mathbb Q$. Vaughan's identity is is a decomposition of $-\zeta'/\zeta$ and here you only have to replace zeta by the Dedekind zeta. | |
| Sep 3, 2020 at 8:24 | comment | added | Daniel Loughran | A more interesting problem seems to be the following. Let $K/\mathbb{Q}$ be a number field. Then is $\{\alpha p\}$ equidistributed as $p$ runs over all primes completely splti in $K$? (Or more general Chebotarev sets.) This doesn't seem to be immediately reducible to Vinogradov's result. | |
| Sep 2, 2020 at 20:07 | comment | added | Daniel Loughran | Yes I had realised this as well. It's a nice trick. | |
| Sep 2, 2020 at 19:28 | comment | added | GH from MO | @DanielLoughran: Thank you. Actually, we don't even need to use Dirichlet characters. The condition $p\equiv a\pmod{q}$ can be detected directly by additive characters modulo $q$, so one arrives at the last display (with different $a$'s) directly. | |
| Sep 2, 2020 at 9:30 | comment | added | Daniel Loughran | Great answer, thanks. | |
| Sep 2, 2020 at 9:30 | vote | accept | Daniel Loughran | ||
| Sep 2, 2020 at 3:26 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Sep 1, 2020 at 21:50 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Sep 1, 2020 at 21:44 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Sep 1, 2020 at 21:39 | history | answered | GH from MO | CC BY-SA 4.0 |