Mahler measure
From Wikipedia, the free encyclopedia
In mathematics, the Mahler measure M(p) of a polynomial p is
Here p is assumed complex-valued and
is the lα norm of p.
It can be shown that if
then
The measure is named after Kurt Mahler.
[edit] Properties
- The Mahler measure is multiplicative, i.e. M(pq) = M(p)M(q).
- If p is an irreducible polynomial with
and M(p) = 1, then p is a cyclotomic polynomial.
[edit] References
- Jensen, J. L. "Sur un nouvel et important théorème de la théorie des fonctions." Acta Mathematica 22, 359–364, 1899.
- Mossinghoff, M. J. "Polynomials with Small Mahler Measure." Mathematics of Computation 67, 1697–1705 and S11–S14, 1998.
