Timeline for Numbers divisible only by primes of the form 4k+1
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 24, 2020 at 22:31 | comment | added | shreevatsa | For completeness, the constant $c$ here (based on the answer to the question by @WillJagy above) should be $1/(4K) \approx 0.327129366941$ where $K \approx 0.764223653589$ is the Landau–Ramanujan constant. (Sort of confirmed by experiment -- it converges very slowly -- e.g. $A(10000000) = 814182 \approx 0.3269 \times 10000000/\sqrt{\log 10000000}$.) | |
| Jul 31, 2016 at 17:36 | comment | added | Greg Martin | You can also look at the Selberg–Delange method, see for example Tenenbaum's "Introduction to Analytic and Probabilistic Number Theory", section II.5 I think. | |
| Jul 30, 2016 at 20:37 | history | edited | stankewicz | CC BY-SA 3.0 |
added 112 characters in body
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| Jul 16, 2016 at 8:12 | vote | accept | user95040 | ||
| Jul 14, 2016 at 1:15 | comment | added | Will Jagy | @JeremyRouse I asked on one of the sites for counting primitively represented $x^2 + y^2,$ it was the same as unrestricted but with a smaller constant, surprised me. I guess this question would simply halve that number because we have even and odd about the same. Let me try to find that. math.stackexchange.com/questions/1282550/… | |
| Jul 14, 2016 at 0:33 | comment | added | Jeremy Rouse | That is the $c$ value for the sums of two squares counting function, which is larger than $A(N)$. | |
| Jul 14, 2016 at 0:10 | comment | added | David E Speyer | $c = \tfrac{1}{\sqrt{2}} \prod_{p \equiv 3 \bmod 4} 1/\sqrt{1-p^{-2}} \approx 0.764$. See mathworld.wolfram.com/Landau-RamanujanConstant.html math.stackexchange.com/questions/264069/… | |
| Jul 13, 2016 at 21:43 | history | answered | stankewicz | CC BY-SA 3.0 |