Timeline for Is there a simple way to compute the number of ways to write a positive integer as the sum of three squares?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Jun 3, 2014 at 23:55 | comment | added | GH from MO | Actually, the nice formula for square-free $n$ generalizes nicely to primitive representations. From this formula, it is straightforward to generate Bateman's formula for all representations. | |
| Apr 27, 2010 at 2:27 | comment | added | Felipe Voloch | Bounds for the class number of imaginary quadratic fields follow from the Brauer-Siegel formula. See e.g. Davenport's book. | |
| Nov 3, 2009 at 6:00 | history | edited | Reid Barton | CC BY-SA 2.5 |
fixed link to mathworld
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| Nov 2, 2009 at 21:33 | comment | added | David E Speyer | Hmmm. Since a positive proportion of integers are square free, you could just concentrate on that case. Then you are asking whether the class number h(n) is less than x*sqrt{n} with positive probability. I'm pretty sure that this is either known or conjectured to be true. | |
| Nov 2, 2009 at 19:48 | comment | added | Michael Lugo | Thanks. It seems that the formulas for the number of ways to write n as a sum of k squares are much simpler when k is even than when k is odd. My conjecture, suitably rewritten, still seems to be true from numerical data: lim (n → ∞) #{k ≤ n and r_j(k)/k^(j/2-1) ≤ x} / n seems to be nontrivial, at least for x in a certain range. I'm now trying to familiarize myself with the literature, which is a daunting task since so many people have studied this... | |
| Nov 1, 2009 at 5:13 | history | answered | David E Speyer | CC BY-SA 2.5 |