Timeline for Overall idea of estimating major arcs in Waring's problem
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Oct 21, 2022 at 11:21 | vote | accept | Gareth Ma | ||
| Oct 20, 2022 at 23:50 | comment | added | Ofir Gorodetsky | If Goldbach is brought up, let me mention K. Soundararajan's notes on additive combinatorics, found on this website, that were recommended to me once. They include a self-contained and very clear (IMO) proof of Vinogradov's 3 primes theorem assuming the Generalized Riemann Hypothesis. This makes the proof quite short (5 pages) and, naturally, removes a lot of the technical issues. | |
| Oct 20, 2022 at 23:21 | comment | added | TravorLZH | By the way, I have written a Chinese article explaining the application of circle method to Goldbach's problem. Hope you will find that one helpful as well. | |
| Oct 20, 2022 at 22:54 | answer | added | TravorLZH | timeline score: 3 | |
| Oct 20, 2022 at 21:42 | comment | added | Gareth Ma | @TravorLZH (Hi Travor I actually emailed you before haha) Yeah Travor I understand what you said so far, and in the text I am referring we will prove that $\int_{\mathfrak{M}} f^s(\alpha) e(-\alpha n) d\alpha \ll n^{s/k - 1}$ while $\int_{\mathfrak{m}} f^s(\alpha) e(-\alpha n) d\alpha = o(n^{s/k - 1})$, which will imply that number of representations is positive for large enough $n$. However, what I am asking in this question is the technicalities of the first estimate, like what are the lemmas used and what does each approximately say/do? (See what I wrote for the minor arcs). Hope you get | |
| Oct 20, 2022 at 16:23 | comment | added | TravorLZH | As a result, the strategy is to give asymptotic estimates for integral over major arcs (collection of these small neighborhoods of rationals) and to give upper bound for integral over minor arcs (i.e. the integral over region in $[0,1]$ that are relatively distant from rationals) | |
| Oct 20, 2022 at 16:22 | comment | added | TravorLZH | The motivation is that the function $f(\alpha)$ has good properties when $\alpha$ is close to some rational number, and it is also true that the integral over some small neighborhoods of rationals turn out to be the constituents of the main term in the asymptotic formula. | |
| Oct 20, 2022 at 14:21 | comment | added | kodlu | please delete the math stack exchange version | |
| Oct 20, 2022 at 13:53 | history | edited | Gareth Ma | CC BY-SA 4.0 |
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| Oct 20, 2022 at 7:21 | history | edited | Gareth Ma | CC BY-SA 4.0 |
added 67 characters in body
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| Oct 20, 2022 at 6:03 | history | edited | YCor | CC BY-SA 4.0 |
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| S Oct 20, 2022 at 5:26 | review | First questions | |||
| Oct 20, 2022 at 6:05 | |||||
| S Oct 20, 2022 at 5:26 | history | asked | Gareth Ma | CC BY-SA 4.0 |