5 problems

Boyd's conjectures. One has $\mu(n)>1$ for every $n\geq6$, and

Let $n\geq 21$ and let $(k,n)$ denote a pair of integers with $k\notin\{0,1,n-1,n\}$. A pair is Newman-admissible if there exists a Newman polynomial of degree $n$ having exactly…

A Newman polynomial is a polynomial whose coefficients are all $0$ or $1$. For a polynomial $Q_N$, let $\deg Q_N$ denote its degree and let $|Q_N|_1$ and $|Q_N^2|_{\infty}$ denote…

The $\pi/4$ extremal constant conjecture. There is a sequence of Newman polynomials $p$ with $p(1)/\deg(p)\to0$ and $R(p)\to\pi/4$, and $\pi/4$ is the best possible limiting consta…

A Newman polynomial is a polynomial whose coefficients are $0$ or $1$. For a polynomial $p(x)=\sum_{j=0}^d p_jx^j$ with $p_d\ne 0$, write … and let $\deg p=d$. Define … Yu's conjec…