Timeline for Asymptotic behavior of a certain sum of ratios of consecutives primes
Current License: CC BY-SA 4.0
12 events
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| Feb 4, 2020 at 10:48 | comment | added | GH from MO | @Lucia: Thanks again! The negative bias might explain why the OP is seeing $2/e$ instead of $1$. I updated my "Added" section. | |
| Feb 4, 2020 at 10:42 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Feb 4, 2020 at 10:40 | comment | added | Lucia | Yes, that's right. A slightly more precise approximation is that ${\frak S}(\{0, h\})$ behaves like $1-1/h$ on average, and the negative secondary contribution shows up in some biases. | |
| Feb 4, 2020 at 10:37 | comment | added | GH from MO | @Lucia: Thanks for your comment! My $2C_2D_h$ is $\mathfrak{S}(\{0,h\})$, and this also has average $1$ because of translation invariance of $\mathfrak{S}(\{h_1,h_2\})$, right? | |
| Feb 4, 2020 at 10:28 | comment | added | Lucia | Hi GH: The singular series constants are $1$ on average -- Hardy-Littlewood probabilities are approximately the same as Cramer probabilities on average. Thus one should have $C=1$ in your final answer. | |
| Feb 4, 2020 at 9:54 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Feb 4, 2020 at 9:42 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Feb 4, 2020 at 9:36 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Feb 4, 2020 at 7:57 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Feb 4, 2020 at 7:47 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Feb 4, 2020 at 7:35 | vote | accept | Augusto Santi | ||
| Feb 4, 2020 at 7:33 | history | answered | GH from MO | CC BY-SA 4.0 |