Height of a polynomial

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In mathematics, the height of a polynomial P with complex coefficients is defined to be the maximum of the magnitudes of its coefficients. For a polynomial P given by

P = a_0 + a_1 x + a_2 x^2 + \cdots + a_k x^k

its height H(P) is given by

H(P) = \underset{i}{\max} \,|a_i|.\,

For a complex polynomial P of degree n, the height H(P) and Mahler measure M(P) are related by the double inequality

\binom{n}{n/2}^{-1} H(P) \le M(P) \le H(P) \sqrt{n+1}

where \scriptstyle \binom{n}{n/2} is the binomial coefficient.

[edit] References

  • Mahler, K., "On two extremum properties of polynomials", Illinois J. Math. 7, 681-701, 1963.

[edit] External links

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