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}
}
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

On representations of integers by indefinite ternary quadratic forms

Mikhail Borovoi
2006
View 7 Excerpts
Highly Influenced

Hardy-Littlewood varieties and semisimple groups

Mikhail Borovoi, Zerv Rudnick z
2005
View 7 Excerpts
Highly Influenced

Density of Integer Points on Affine Homogeneous Varieties

W..., Duke, +3 authors SARNAK
1993
View 2 Excerpts
Highly Influenced

Mixing

A. Eskin, C. McMullen
counting, and equidistribution in Lie groups. Duke Math. J. 71 • 1993
View 2 Excerpts
Highly Influenced

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

J.-L. Colliot-Thélène, F. Xu
Compositio Math. 145 • 2009
View 2 Excerpts

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