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arXiv · 1802.00792

Values of Random Polynomials at Integer Points

Jayadev S. Athreya·Gregory Margulis
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Abstract

Using classical results of Rogers bounding the $L^2$-norm of Siegel transforms, we give bounds on the heights of approximate integral solutions of quadratic equations and error terms in the quantiative Oppenheim theorem of Eskin-Margulis-Mozes for almost every quadratic form. Further applications yield quantitative information on the distribution of values of random polynomials at integral points.

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Jayadev S. Athreya, Gregory Margulis. 2018-02-02. Values of Random Polynomials at Integer Points. https://arxiv.org/abs/1802.00792

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