Analytic number theory | Polynomials

Mahler measure

In mathematics, the Mahler measure of a polynomial with complex coefficients is defined as where factorizes over the complex numbers 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 for on the unit circle (i.e., ): By extension, the Mahler measure of an algebraic number is defined as the Mahler measure of the minimal polynomial of over . In particular, if is a Pisot number or a Salem number, then its Mahler measure is simply . The Mahler measure is named after the German-born Australian mathematician Kurt Mahler. (Wikipedia).

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Related pages

Coefficient | Associated prime | Automorphism | Minimal polynomial (field theory) | Topological entropy | Algebraic number | Geometric mean | Duality (mathematics) | Polynomial | The Art of Computer Programming | Salem number | Bombieri norm | Journal of Number Theory | Ergodic theory | Perron number | Mathematics | Unit circle | Riemann zeta function | Cyclic module | Kurt Mahler | Ring (mathematics) | Cyclotomic polynomial | Dirichlet L-function | Lehmer's conjecture | Complex number | Jensen's formula | Principal ideal | Module (mathematics) | Kronecker's theorem