Timeline for Is the class number of the quadratic field $x^2=3\cdot2^n+1$ $O(n)$?
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| Oct 29, 2011 at 15:16 | comment | added | Kevin Buzzard | I'm no expert, but I suspect that the reason that the class numbers seem, vaguely, to be going "big small big small..." alternately in the Mersenne list is that, when $n=2m$ is even, you get a unit $u=2^m+x$ of about as small a height as you could ever hope for, which makes the regulator small so the class group has to be big by Brauer-Siegel. | |
| Oct 29, 2011 at 13:57 | comment | added | Damian Rössler | The Brauer-Siegel theorem gives some information on the asymptotics of the class number in this situation ( see en.wikipedia.org/wiki/Brauer-Siegel_theorem ). Note that to apply it in your situation, you would have to get some hold on the regulators of your sequence of quadratics fields. | |
| Oct 29, 2011 at 13:41 | history | edited | joro | CC BY-SA 3.0 |
Added Mersenne numbers
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| Oct 29, 2011 at 13:14 | history | asked | joro | CC BY-SA 3.0 |