Values of random polynomials at integer points
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Athreya, Jayadev S.; Margulis, Gregory;
Values of random polynomials at integer points
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.
to appear, Journal of Modern Dynamics
- Yale University United States
- University of Maryland, College Park United States
- University of Illinois at Urbana-Champaign United States
- Mathematical Sciences Research Institute United States
- University of Mary Washington United States
Mathematics - Number Theory, 11H60, 11P21, 11C08, FOS: Mathematics, Number Theory (math.NT)
Mathematics - Number Theory, 11H60, 11P21, 11C08, FOS: Mathematics, Number Theory (math.NT)
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These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
Citations provided by BIP!popularityPopularity provided by BIP!
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
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