Siegel transforms are maps sending bounded and compactly supported functions on the d-dimensional real vector space to integrable functions on the space of lattices. The k-th moment formula for a Siegel transform is an integral formula for the k-th power of the Siegel transform over the space of lattices, by using integrals defined over the vector space. Moment formulas, firstly studied by Rogers, make it possible to employ method of moments from probabilistic to study the distribution of lattice points in large dimensions.

For the primitive Siegel transform, which is relative to the study of distribution of primitive lattice points, only first and second moment formulas are known. In this talk, we will discuss the possibility of obtaining applications using method of moments, without having higher moment formulas.