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), 298-316. (doi:10.1006/jnth.1996.0079).
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Description/Abstract
Letψ(r),r=1, 2, … be a positive decreasing sequence such that ∑r=1∞ ψ(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 |
|---|---|
| ISSNs: | 0022-314X (print) |
| Related URLs: | |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | University Structure - Pre August 2011 > School of Mathematics > Applied Mathematics |
| Item ID: | 29146 |
| Date Deposited: | 22 Dec 2006 |
| Last Modified: | 01 Jun 2011 08:56 |
| Contributors: | Dodson, M.M. (Author) Rynne, B.P. (Author) Vickers, J.A.G. (Author) |
| Date: | 1996 |
| Status: | Published |
| URI: | http://eprints.soton.ac.uk/id/eprint/29146 |
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