Kneser's theorem (combinatorics): Difference between revisions

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==Restricted results==

#REDIRECT [[User:Deltahedron/Minkowski's second theorem]]

Stronger results are known for restricted classes of polynomials or algebraic numbers.

If ''P''(''x'') is not reciprocal then

:<math>M(P) \ge M(x^3 -x - 1) \approx 1.3247 </math>

and this is clearly best possible.<ref name=S328>Smyth (2008) p.328</ref> If further all the coefficients of ''P'' are odd then<ref name=S329/>

:<math>M(P) \ge M(x^2 -x - 1) \approx 1.618 . </math>

If the field '''Q'''(α) is Galois over '''Q''' then Lehmer's conjecture holds.<ref name=S329>Smyth (2008) p.329</ref>

==References==

{{Reflist}}

* {{cite book | first=Chris | last=Smyth | chapter=The Mahler measure of algebraic numbers: a survey | pages=322–349 | editor1-first=James | editor1-last=McKee | editor2-last=Smyth | editor2-first=Chris | title=Number Theory and Polynomials | series=London Mathematical Society Lecture Note Series | volume=352 | publisher=[[Cambridge University Press]] | year=2008 | isbn=978-0-521-71467-9 }}