Timeline for Where to cut off a double sum?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 16, 2021 at 20:58 | comment | added | H A Helfgott | Hah - of course I was miscalculating. The bound $|U|\leq 6 M^{2/5}$ in the above should be $|U|\leq 5 M^{2/5}$ (and there was likely an error elsewhere - $\alpha \approx 7$ is too far off). The argument you've given is obviously correct, and $\alpha=2$ is indeed optimal. | |
| Dec 16, 2021 at 12:39 | comment | added | H A Helfgott | Hm, you are right - I am now wondering what I am doing wrong. | |
| Dec 16, 2021 at 12:30 | comment | added | Sean Eberhard | This doesn't seem plausible (or I don't understand the question). Suppose I can always compute the tail bound $\sum_{(m, n) \in U^c} 1/(m^2 n^2 \max(m, n))$ exactly and efficiently, for whatever set $U$. Suppose I have computed some $N$ terms of the sum exactly, and I'm deciding which is the best $(N+1)$th term to compute to minimize the error. Plainly, the answer is to minimize $m^2 n^2 \max(m, n)$. | |
| Dec 16, 2021 at 11:47 | comment | added | H A Helfgott | PS. I'd be interested in the same question with $(m+n)$ instead of $\max(m,n)$ (that's in fact closer to my "real" application) - that seems a bit harder, though. | |
| Dec 16, 2021 at 11:43 | history | edited | Sean Eberhard | CC BY-SA 4.0 |
replaced an instance of $U$ with its complement
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| Dec 16, 2021 at 11:20 | history | asked | H A Helfgott | CC BY-SA 4.0 |