# Linnik's problem in fiber bundles over quadratic homogeneous varieties

@inproceedings{Bersudsky2021LinniksPI, title={Linnik's problem in fiber bundles over quadratic homogeneous varieties}, author={Michael Bersudsky and Uri Shapira}, year={2021} }

We compute the statistics of SLd(Z) matrices lying on level sets of an integral polynomial defined on SLd(R), a result that is a variant of the well known theorem proved by Linnik about the equidistribution of radially projected integral vectors from a large sphere into the unit sphere. Using the above result we generalize the work of Aka, Einsiedler and Shapira in various directions. For example, we compute the joint distribution of the residue classes modulo q and the properly normalized…

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