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).

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Description/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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1006/jnth.1996.0079
ISSNs: 0022-314X (print)
Subjects:
ePrint ID: 29146
Date :
Date Event
1996Published
Date Deposited: 22 Dec 2006
Last Modified: 16 Apr 2017 22:23
Further Information:Google Scholar
URI: http://eprints.soton.ac.uk/id/eprint/29146

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