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).


Full text not available from this repository.

Original Publication URL:


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)
Related URLs:
Subjects: Q Science > QA Mathematics
Divisions : University Structure - Pre August 2011 > School of Mathematics > Applied Mathematics
ePrint ID: 29146
Accepted Date and Publication Date:
Date Deposited: 22 Dec 2006
Last Modified: 31 Mar 2016 11:54

Actions (login required)

View Item View Item