4 problems

For odd integers $n$, let $\alpha_n$ be the Gaussian-period algebraic integer and let $C_{\kappa(n)}$ be the associated cyclovariety, with Mahler measures denoted by…

Let $\alpha_n$ be the Gaussian-period algebraic integer defined in the paper, and let $\mathrm{m}(\alpha_n)$ denote its Mahler measure. For a property of odd integers $n$, say that…

Let $(s_k(n))_{k\geq 0}$ be the sequence associated with the positive integer $n$. For a fixed $n$, define $(k_N)_{N\geq 1}$ by requiring that $s_{k_N}(n)$ is the $N$th prime term…

Fix an integer $a$, and consider the hyper-plane $z=a$ in the space of Hurwitz integers. Let $r$ denote the radius of a ball and count the Hurwitz primes lying in that hyper-plane…