The aim of this paper is to introduce the analogues of the restrictions of $z\to z^k$, $k\in\mathbf{Z}$, $z\in\mathbf{C}$, to the unit circle, in the case of the unit sphere $\partial B(0,1)$ in $\mathbf{R}^{m+1}$ and to apply them to boundary value problems of left monogenic functions in $\mathbf{R}^{m+1}\backslash \partial B(0,1)$.

Discriminants of equations up to the ninth degree are calculated by using a computer. The numbers of terms included in the discriminants are 2, 5, 16, 59, 246, 1103, 5247, and 26059 for equations of degree two, three, four, five, six, seven, eight, and nine, respectively. Expressions of discriminants up to the fifth degree are included in this paper.