Effective Limit Distribution of the Frobenius Numbers

Effective Limit Distribution of the Frobenius Numbers

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Han Li, Yale University
Fine Hall 801

The Frobenius number of a lattice point $\bf{a}$ with positive coprime coordinates, is the largest integer which can NOT be expressed as a non-negative integer linear combination of the coordinates of $\bf{a}$. Marklof showed in 2010 that the limit distribution of the Frobenius numbers is given by the distribution for the covering radius function of a random unimodular lattice. The aim of the talk is to discuss the reason of this phenomenon, and indicate how to obtain the rate of the convergence of the corresponding distribution functions.