Timeline for Old question of Serre on discriminants of a sequence of polynomials
Current License: CC BY-SA 2.5
3 events
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| Aug 8, 2014 at 15:12 | comment | added | Vesselin Dimitrov | I think the polynomial $x^d-x-1$ disproves the statement in the last paragraph (the possible refinement of Lehmer's conjecture). If I am not mistaken, its discriminant is $d^d + (-1)^{d}(d-1)^{d-1}$. The Chebyshev polynomials (normalized: take the minimum polynomial of $\zeta_n+\zeta_n^{-1}$) are another counterexample, although this is closer to the cyclotomic examples and may still be considered "essentially cyclotomic." | |
| Jan 17, 2011 at 5:38 | vote | accept | Luis H Gallardo | ||
| Jan 14, 2011 at 17:05 | history | answered | user631 | CC BY-SA 2.5 |