  Littlewood polynomials are polynomials with each of their coefficients in
{-1,1}. A sequence of Littlewood polynomials that satisfies a remarkable
flatness property on the unit circle of the complex plane is given by the
Rudin-Shapiro polynomials. It is shown in this paper that the Mahler measure
and the maximum modulus of the Rudin-Shapiro polynomials on the unit circle of
the complex plane have the same size. It is also shown that the Mahler measure
and the maximum norm of the Rudin-Shapiro polynomials have the same size even
on not too small subarcs of the unit circle of the complex plane. Not even
nontrivial lower bounds for the Mahler measure of the Rudin Shapiro polynomials
have been known before.
