Timeline for What is the distribution of the $L^\infty$ norm of minimal polynomials of numbers in a number field?
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| Apr 9, 2010 at 11:26 | comment | added | Dror Speiser | @Gerry: Both $A(x)$ and $B(x)$ are $\sim c_i x^2$ for some constants, and this will be true for any quadratic field, where constant will depend on discriminant, class number, and regulator. But, for a non-quadratic number field, the coefficients of the minimal polynomial of the generic number given in a $\mathbb{Q}$-basis, will be of high degree, and I can't see why the same asymptotic behavior should remain - even though it probably will. | |
| Apr 8, 2010 at 23:39 | comment | added | Gerry Myerson | Have you tried a (possibly) simple case, like $K={\bf Q}(i)$? | |
| Apr 8, 2010 at 23:08 | history | edited | Dror Speiser | CC BY-SA 2.5 |
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| Apr 8, 2010 at 23:02 | history | edited | Dror Speiser | CC BY-SA 2.5 |
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| Apr 8, 2010 at 22:53 | history | asked | Dror Speiser | CC BY-SA 2.5 |