6 problems

Let … be a polynomial with fixed outer coefficients $a_n=1$ and $a_0=b$, and let $E_{n,b}(H)$ denote the number of such polynomials of height at most $H$ whose Galois group is not…

Let $q$ be a fixed power of an odd prime and let $c>0$ be fixed. For any polynomial $F\in\mathbb{F}_q[x][T]$ that is separable in the variable $T$, define the Liouville function by…

Let … be the degree-six truncation of the binomial expansion, and let $\mathfrak{S}_6$ denote the full symmetric group on six symbols. Filaseta–Moy conjecture. The Galois group of…

For $m\geq 2$ and $n\geq 1$, let $P_{m,n}$ denote the multiplier polynomial in the quadratic case $d=2$. A polynomial is called 2-special when it has the special coefficient and di…

Throughout, let $q$ be a prime power, let $I_q$ be the set of all monic irreducible polynomials in $\mathbb{F}_q[x]$, and call a subset $A$ of $I_q$ an $F$-set if, for every…

Let ${\mathbb F_q}[t]$ be the polynomial ring over the finite field ${\mathbb F_q}$. For a set ${\mathcal H}\subset {\mathbb F_q}[t]\setminus\{0\}$, being van der Corput means that…