Effective Equidistribution on Hilbert Modular Varieties

Abstract

We compute effective error rates for the equidistribution of translates of diagonal orbits on Hilbert modular varieties. The translation is determined by n real parameters and our results require the assumption that all parameters are non-zero. The error rate is given in explicit polynomial terms of the translation parameters and Sobolev type norms of the test functions. The effective equidistribution is applied to give counting estimates for binary quadratic forms of square discriminant over real number rings.