9 problems

Let $P(x)\in\mathbb{Z}[x]$ be a monic irreducible polynomial, and let $m_{\mathbb{H}}(P)$ denote its quaternionic Mahler measure. Quaternionic Lehmer conjecture. There is a constan…

Let $D$ be a symmetric slice domain in the quaternions, and let $\mathcal{O}_s(D)$ denote the integral domain of slice-preserving regular functions on $D$, with quotient field…

Let $A\in\mathcal{M}_n(\mathbb{C})$ be an $n\times n$ complex matrix. Its quaternionic numerical range is…

The paper constructs invariant $n$-multiplications on quaternionic algebras, including the quaternionic algebra $\textit{{\fontencoding{OT2}\fontfamily{wncyr}\selectfont Zh}}$ and…

Transient quaternionic motion conjecture. Motion in the dimensions outside the complex plane is typically transient: the particle trajectories bring the zeros back together, after…

Let $\Omega$ be a domain with smooth boundary in the quaternionic space $\mathbb{H}$, and let $H^1_{(k)}(\Omega)$ denote the first cohomology group of the $k$-Cauchy–Fueter complex…

Involution invariance conjecture. The involution $f\mapsto f^*$ preserves $\mathcal N(\Omega_1)$ without assuming that $\Omega_1$ is simply connected.

Let $\mathfrak p$ denote the operator introduced through the quaternionic formulation of the field equations, and decompose its action into linear and nonlinear parts. The linear p…

The paper studies holomorphic functions on the complexified quaternionic space $\mathbb H_{\mathbb C}=\mathbb C\otimes\mathbb H$ and identifies certain Feynman integrals with inter…