Timeline for What keeps asymptotic Goldbach's conjecture out of reach of current technology?
Current License: CC BY-SA 4.0
10 events
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| Dec 23, 2020 at 0:25 | comment | added | user267839 | So my question is if the latter expression for $S(\alpha)$ was wrong or are they both equal. Indeed in the question mathoverflow.net/questions/379543/… I'm asking exactly about the problem. By kodlu's hints we can obtain the first extression but the question is if the second expression equals to first one or is wrong? | |
| Dec 23, 2020 at 0:24 | comment | added | user267839 | A curios question about the sum $S(\alpha)=\sum_{a=0} ^{q-1} e \left( \frac{ap}{q} \right) \underset{n\equiv a\pmod{q}}{\sum_{n\leq N}} \Lambda(n)$ Before Alex M. edited Jan's answer the sum was given by $\sum_{(a,q)=1} e(\frac{ap}{q})\underset{n\equiv a\pmod{q}}{\sum_{n\leq N}} \Lambda(n)$ | |
| S Dec 22, 2020 at 22:16 | history | edited | Alex M. | CC BY-SA 4.0 |
added 18 characters in body
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| Dec 22, 2020 at 21:46 | review | Suggested edits | |||
| S Dec 22, 2020 at 22:16 | |||||
| Oct 31, 2019 at 14:37 | comment | added | Sylvain JULIEN | Sorry for digging out this old question, but I would have something to ask that may serve as an insight to the "(expected) cancellation inside the integral". Isn't the isobarycenter of the values $e(-N\alpha)$ close to 0 ? I guess the set of those values has a non trivial symmetry group, and that at least a pairwise cancellation of the considered exponential can be reached for most values of $N$. Does such a rough idea have any interest? | |
| Oct 29, 2014 at 16:46 | comment | added | Sylvain JULIEN | I don't doubt it. I just meant to point out the huge technical aspect of mathematicians' ideas, while the physicists' ones, though more simple, lack rigor. | |
| Oct 29, 2014 at 16:36 | comment | added | tracing | @SylvainJULIEN: Green and Tao have a major theorem devoted to proving essentially best possible results about solving linear equations in primes (such as Goldbach, which is the equation $p_1 + p_2 = N$) which don't (explicitly or implicitly) include single equations in two variables (such as Goldbach or twin primes) inside them (so their results, in the end, don't address Goldbach or twin primes). So I think it's safe to assume that Terry has devoted a lot of effort to understanding the difficulties in Goldbach and twin primes ... . | |
| Apr 1, 2014 at 18:19 | vote | accept | Sylvain JULIEN | ||
| Apr 1, 2014 at 18:16 | comment | added | Sylvain JULIEN | Ok, thank you for your answer. I know I still think like a physicist, but to me these approaches look rather technical, involving a quite heavy machinery for the results one can get through it. I wish someone brilliant and both intuitive and rigorous like Terry Tao could turn my heuristic arguments developped in threads like "About Goldbach's conjecture" into a proper proof. Referring to this last question, a rigorous proof that the quantity denoted by $\alpha_{n}$ is an $o(n)$ would already be interesting. I have no idea of how to achieve this though. | |
| Apr 1, 2014 at 17:51 | history | answered | Jan-Christoph Schlage-Puchta | CC BY-SA 3.0 |