Mahler Measure

In mathematics, the Mahler measure M(p) of a polynomial p is

Here p is assumed complex-valued and

is the Lτ norm of p (although this is not a true norm for values of τ < 1).

It can be shown that if

then

The Mahler measure of an algebraic number α is defined as the Mahler measure of the minimal polynomial of α over Q.

The measure is named after Kurt Mahler.

Read more about Mahler Measure:  Properties

Famous quotes containing the words mahler and/or measure:

    I seemed intent on making it as difficult for myself as possible to pursue my “male” career goal. I not only procrastinated endlessly, submitting my medical school application at the very last minute, but continued to crave a conventional female role even as I moved ahead with my “male” pursuits.
    —Margaret S. Mahler (1897–1985)

    Both the man of science and the man of art live always at the edge of mystery, surrounded by it. Both, as a measure of their creation, have always had to do with the harmonization of what is new with what is familiar, with the balance between novelty and synthesis, with the struggle to make partial order in total chaos.... This cannot be an easy life.
    J. Robert Oppenheimer (1904–1967)