3 problems

Let $q$ be an odd prime power, let $\beta$ be a primitive element of $\mathbb F_{q^2}$, and define … for $r\in\mathbb F_q$. Set … and let $\mathcal U_{\beta}$ be the…

Let $\mathrm{SO}(3)$ denote the rotation group. A quadrature formula on $\mathrm{SO}(3)$ with equal weights is said to reproduce integrals of polynomials of degree at most $2$ exac…

An exact $t$-design is a collection of vectors reproducing the relevant $t$-th moments of the uniform distribution, and Kuperberg's construction uses only…