We give a classification of irreducible symmetric spaces which admit standard compact Clifford–Klein forms. The method uses representation theory over the real number field and the criterion for properness and cocompactness of the action on homogeneous spaces due to T. Kobayashi.

It is known that the multiple sine function for a “rational” period satisfies an algebraic differential equation. However, for a non-“rational” period, the differential algebraicity of the multiple sine function is obscure. In this paper, we prove that, if there exists a non-real element in the set $\{\omega_{j}/\omega_{i}|1\leq i<j\leq r\}$, the multiple sine function $\text{Sin}_{r}(x,(\omega_{1},\cdots,\omega_{r}))$ does not satisfy any algebraic differential equation.