Details of Grant 

EPSRC Reference:	GR/N63659/01
Title:	METRIC DIOPHANTINE APPROXIMATION ON MANIFOLDS
Principal Investigator:	Dodson, Professor MM
Other Investigators:
Researcher Co-Investigators:
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Department:	Mathematics
Organisation:	University of York
Scheme:	Standard Research (Pre-FEC)
Starts:	07 August 2000	Ends:	06 October 2000	Value (£):	3,850
EPSRC Research Topic Classifications:	Algebra & Geometry
EPSRC Industrial Sector Classifications:
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Summary on Grant Application Form
The objective of the visit is to investigate the possibility of building on recent advances in metric Diophantine approximation on manifolds by refining and applying the techniques involved. In particular a quantitative version of the analogue of the Khintchine-Groshev theorem for points on a smooth planar curve with non-zero curvature almost everywhere will be sought in terms of an asymptotic formula for the number of solutions of the Diophantine inequality satisfied by points on the curve. In this case the techniques will be based on a powerful general approach that has been used with some success in a related problem. By specialising to the relatively simple case under consideration, most (but not all!) of the geometric pathologies that prevent establishing the formula cannot occur. Approaches to solving other questions would also be considered.
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Organisation Website:	http://www.york.ac.uk