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Small fractional parts of quadratic forms in many variables
Published online by Cambridge University Press: 26 February 2010
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Let
be a real quadratic form in n variables x1,…, xn and let ‖θ‖ denote the distance from θ to the nearest integer. Danicic [3] proved that if N > 1 and ξ > 0 then there exist integers x1,…, xn, not all zero, satisfying
where C depends on n and ξ only.
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