Height of a polynomial

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In mathematics, the height and length of a polynomial P with complex coefficients are measures of its "size".

Definition[edit]

For a polynomial P of degree n given by

the height H(P) is defined to be the maximum of the magnitudes of its coefficients:

and the length L(P) is similarly defined as the sum of the magnitudes of the coefficients:

Relation to Mahler measure[edit]

The Mahler measure M(P) of P is also a measure of the size of P. The three functions H(P), L(P) and M(P) are related by the inequalities

where is the binomial coefficient.

References[edit]

External links[edit]