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Simultaneous Diophantine approximation and asymptotic formulae on manifolds

Dodson, M.M., Rynne, B.P. and Vickers, J.A.G. (1996) Simultaneous Diophantine approximation and asymptotic formulae on manifolds Journal of Number Theory, 58, (2), pp. 298-316. (doi:10.1006/jnth.1996.0079).

Record type: Article

Abstract

Let?(r),r=1, 2, … be a positive decreasing sequence such that ?r=1? ?(r)kdiverges. Using a powerful variance argument due to Schmidt, an asymptotic formula is obtained for the number of integer solutions q of the system of Diophantine inequalities[formula]which holds for almost all points (x1, …, xk) on a smoothm-dimensional submanifoldMof k. The manifold satisfies certain curvature conditions which entail restrictions on the codimension. This result extends the known result when the 0?points are not constrained to lie in a submanifold, (i.e., whenM=k) to a reasonably general class of manifolds.

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Published date: 1996

Identifiers

Local EPrints ID: 29146
URI: http://eprints.soton.ac.uk/id/eprint/29146
ISSN: 0022-314X
PURE UUID: d1958a5f-225e-4772-bed3-539a7dc2329a

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Date deposited: 22 Dec 2006
Last modified: 17 Jul 2017 15:58

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Contributors

Author: M.M. Dodson
Author: B.P. Rynne
Author: J.A.G. Vickers

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