Baker–Montgomery conjecture on zeros of Fekete polynomials

Let $D$ be a fundamental discriminant, and let $N_D$ denote the number of zeros of the Fekete polynomial $F_D$ in $(0,1)$. Baker–Montgomery conjecture. For almost all fundamental discriminants $D$,

$$N_D\asymp \log\log |D|.$$

This conjecture gives a strong quantitative refinement of the failure of Fekete's conjecture, which asserted that $F_D$ has no zeros in $(0,1)$ for sufficiently large $D$. Baker and Montgomery proved only that $N_D\geq K$ for every fixed integer $K\geq1$ for almost all fundamental discriminants; the stated order of magnitude remains unresolved in the supplied text.