Hi,

In Remark 2 of "Zeros of Fekete Polynomials", (http://arxiv.org/PS_cache/math/pdf/9906/9906214v1.pdf), Conrey et. al. give
$\sup_{|z|=1}|f(z)| \ll p^{0.5} \log p$.

But the Mahler measure of $f$, $M(f)$, is bounded from above by $\sup_{|z|=1}|f(z)|$. (I took this from (7.2) of "Experimental Number Theory by F. R. Villegas.)

Since Mahler measure is multiplicative, then, letting
$$
f = \prod_i f_i
$$
where the product is over all irreducible factors, one has
$$
M(f) = \prod_i M(f_i).
$$

Using lower bounds for Mahler measures found in "The Mahler measure of Algebraic Numbers: A Survey",(http://www.maths.ed.ac.uk/~chris/Smyth240707.pdf), perhaps one can, comparing upper and lower bounds for Mahler measures, get a nontrivial upper bound on the number of irreducible factors of the Fekete polynomial?