  We show that there is an absolute constant $c > 1/2$ such that the Mahler
measure of the Fekete polynomials $f_p$ of the form $$f_p(z) :=
\sum_{k=1}^{p-1}{\left( \frac kp \right)z^k}\,,$$ (where the coefficients are
the usual Legendre symbols) is at least $c\sqrt{p}$ for all sufficiently large
primes $p$. This improves the lower bound $\left(\frac 12 -
\varepsilon\right)\sqrt{p}$ known before for the Mahler measure of the Fekete
polynomials $f_p$ for all sufficiently large primes $p \geq c_{\varepsilon}$.
Our approach is based on the study of the zeros of the Fekete polynomials on
the unit circle.
