# Power-free Values of Polynomials on Symmetric Varieties

@inproceedings{Browning2017PowerfreeVO, title={Power-free Values of Polynomials on Symmetric Varieties}, author={Tim D. Browning and Alexander Gorodnik}, year={2017} }

- Published 2017

Given a symmetric variety Y defined over Q and a non-zero polynomial with integer coefficients, we use techniques from homogeneous dynamics to establish conditions under which the polynomial can be made r-free for a Zariski dense set of integral points on Y . We also establish an asymptotic counting formula for this set. In the special case that Y is a quadric hypersurface, we give explicit bounds on the size of r by combining the argument with a uniform upper bound for the density of integral… CONTINUE READING

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Showing 1-10 of 26 references

## Prime and Almost Prime Integral Points on Principal Homogeneous Spaces by Amos Nevo and Peter Sarnak

View 6 Excerpts

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## On representations of integers by indefinite ternary quadratic forms

View 7 Excerpts

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## Hardy-Littlewood varieties and semisimple groups

View 7 Excerpts

Highly Influenced

## Density of Integer Points on Affine Homogeneous Varieties

View 2 Excerpts

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## Mixing

View 2 Excerpts

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## Brauer–Manin obstruction for integral points of homogeneous spaces and representation by integral quadratic forms

View 2 Excerpts