Dani, Shrikrishna G. (2008) Simultaneous diophantine approximation with quadratic and linear forms Journal of Modern Dynamics (JMD), 2 (1). pp. 129-138. ISSN 1930-5311
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Official URL: http://aimsciences.org/journals/displayArticles.js...
Related URL: http://dx.doi.org/10.3934/jmd.2008.2.129
Abstract
Let Q be a nondegenerate indefinite quadratic form on Rn, n≥3, which is not a scalar multiple of a rational quadratic form, and let CQ={v∈Rn|Q(v)=0}. We show that given v1∈CQ, for almost all v∈CQ\Rv1 the following holds: for any a∈R, any affine plane P parallel to the plane of v1 and v, and ∈>0 there exist primitive integral n-tuples x within ∈ distance of P for which |Q(x)-a|<∈. An analogous result is also proved for almost all lines on CQ.
Item Type: | Article |
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Source: | Copyright of this article belongs to American Institute of Mathematical Sciences. |
Keywords: | Values of Quadratic Forms; Diophantine Approximation; Flows On Homogeneous Spaces |
ID Code: | 74517 |
Deposited On: | 16 Dec 2011 09:26 |
Last Modified: | 18 May 2016 18:53 |
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