Effective Limit Distribution of the Frobenius Numbers

The Frobenius number $F(\text{ba})$ of a lattice point $\text{ba}$ in ${\mathbb{R}}^d$ with positive coprime coordinates, is the largest integer which can $not$ be expressed as a non-negative integer linear combination of the coordinates of $\text{ba}$. Marklof in \cite{M} proved the existence of the limit distribution of the Frobenius numbers, when $\text{ba}$ is taken to be random in an enlarging domain in ${\mathbb{R}}^d$. We will show that if the domain has piecewise smooth boundary, the error term for the convergence of the distribution functions is at most a polynomial in the enlarging factor.