1 Answers
In mathematics, the Mahler measure M {\displaystyle M} of a polynomial p {\displaystyle p} with complex coefficients is defined as
The Mahler measure can be viewed as a kind of height function. Using Jensen's formula, it can be proved that this measure is also equal to the geometric mean of | p | {\displaystyle |p|} for z {\displaystyle z} on the unit circle :
By extension, the Mahler measure of an algebraic number α {\displaystyle \alpha } is defined as the Mahler measure of the minimal polynomial of α {\displaystyle \alpha } over Q {\displaystyle \mathbb {Q} }. In particular, if α {\displaystyle \alpha } is a Pisot number or a Salem number, then its Mahler measure is simply α {\displaystyle \alpha }.