3 problems

Let $a,b,d$ be the minimizers of Problem, and let $\mathbf A,\mathbf B\in\mathbb R[[X,Y]]$ be the series associated to $a$ and $b$, respectively. Let $\mathcal C^{[1/3,2/3]}$ and…

Let $n$, $m$, and $\alpha$ and the notation above be given. Let $\mathcal{P}_S$ be the set of smooth elements of the multiplicative semigroup $\mathcal{P}$, and let…

Let $f$ be an irreducible polynomial and $g$ a linear polynomial, with associated binary forms $F$ and $G$. Let $\alpha(f)$ denote Murphy's alpha value, computed from the numbers o…