5 problems

For a fundamental discriminant $d$, let $F_d(z):=\sum_{n=1}^{|d|-1}\chi_d(n)z^n$ be the Fekete polynomial associated to $d$, where $\chi_d$ is the primitive quadratic character att…

Let $p$ and $q$ be distinct odd primes and set $n=pq$. Let $f_n$ and $g_n$ denote the reciprocal Fekete polynomial and its trace polynomial, respectively. Semiprime Fekete irreduci…

Let $n$ be a positive squarefree integer, let $d>1$ be an integer not dividing $n$, set $d_1=\gcd(d,n)$, and let … Let $F_n$ be the Fekete polynomial and let…

Let $p$ be a prime, let $f_p$ be the polynomial studied in the source, let $g_p$ be its associated auxiliary polynomial, and write … Let $\mathbb Q(f_p)$ denote the splitting field…

For each odd prime $p$, define the Fekete polynomial … where $\left(\frac{a}{p}\right)$ is the Legendre symbol. Fekete's conjecture. The polynomial $F_p(x)$ has no real roots in th…