3 problems

Borwein's conjecture. Its coefficients have a repeating sign pattern of $+--$. This conjecture is known as Borwein's conjecture and was proved by Wang in 2019 using an analytical m…

Ulas's conjecture. For every $\varepsilon>0$ and every $m\geq 2$, there exists $N$, possibly depending on $\varepsilon$ and $m$, such that

Let $D_n(x)$ be the polynomial whose leftmost zero is denoted by $z_n^*$, and let $c_{\mathrm{even}}$ and $c_{\mathrm{odd}}$ be the constants appearing in the asymptotic formulas b…